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

Percentage Accurate: 85.5% → 93.2%

Time: 31.2s

Alternatives: 24

Speedup: 0.9×

• 50.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+298}:\\ \;\;\;\;t\_1 - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

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) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
          (* i (* x 4.0)))))
   (if (<= t_1 (- INFINITY))
     (-
      (+ (+ (* y (* x (* 18.0 (* t z)))) (* a (* t -4.0))) (* b c))
      (+ (* x (* i 4.0)) (* j (* k 27.0))))
     (if (<= t_1 1e+298)
       (- t_1 (* k (* j 27.0)))
       (if (<= t_1 INFINITY)
         (-
          (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
          (* 4.0 (* x i)))
         (* x (- (* 18.0 (* t (* y z))) (* 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else if (t_1 <= 1e+298) {
		tmp = t_1 - (k * (j * 27.0));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	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 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else if (t_1 <= 1e+298) {
		tmp = t_1 - (k * (j * 27.0));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	elif t_1 <= 1e+298:
		tmp = t_1 - (k * (j * 27.0))
	elif t_1 <= math.inf:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(y * Float64(x * Float64(18.0 * Float64(t * z)))) + Float64(a * Float64(t * -4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	elseif (t_1 <= 1e+298)
		tmp = Float64(t_1 - Float64(k * Float64(j * 27.0)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	elseif (t_1 <= 1e+298)
		tmp = t_1 - (k * (j * 27.0));
	elseif (t_1 <= Inf)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(y * N[(x * N[(18.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+298], N[(t$95$1 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 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

   1. Initial program 76.5%

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

   3. Simplified 89.2%

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

      1. associate-*r* 76.5%

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

      2. distribute-rgt-out-- 76.5%

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

      3. sub-neg 76.5%

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

      4. associate-*l* 78.0%

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

      5. *-commutative 78.0%

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

      6. *-commutative 78.0%

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

   6. Applied egg-rr 78.0%

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

      1. sub-neg 78.0%

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

      2. associate-*r* 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*l* 90.7%

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

      5. *-commutative 90.7%

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

      6. fma-neg 90.7%

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

      7. *-commutative 90.7%

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

      8. *-commutative 90.7%

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

      9. associate-*l* 88.8%

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

      10. *-commutative 88.8%

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

      11. distribute-rgt-neg-in 88.8%

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

      12. distribute-lft-neg-in 88.8%

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

      13. metadata-eval 88.8%

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

   8. Simplified 88.8%

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

      1. fma-undefine 88.8%

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

      2. associate-*l* 88.8%

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

      3. *-commutative 88.8%

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

   10. Applied egg-rr 88.8%

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

   if -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)) < 9.9999999999999996e297

   1. Initial program 99.8%

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

   if 9.9999999999999996e297 < (-.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 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in j around 0 89.2%

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

   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 21.1%

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

   5. Taylor expanded in x around inf 79.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq -\infty:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 10^{+298}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq \infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+59} \lor \neg \left(t \leq 2 \cdot 10^{-103}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.5e+59) (not (<= t 2e-103)))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
    (* j (* k -27.0)))
   (-
    (+ (+ (* y (* x (* 18.0 (* t z)))) (* a (* t -4.0))) (* b c))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.5e+59) || !(t <= 2e-103)) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + (j * (k * -27.0));
	} else {
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.5e+59) || !(t <= 2e-103))
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(y * Float64(x * Float64(18.0 * Float64(t * z)))) + Float64(a * Float64(t * -4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.5e+59], N[Not[LessEqual[t, 2e-103]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * N[(x * N[(18.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999999e59 or 1.99999999999999992e-103 < t

   1. Initial program 81.2%

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

   3. Simplified 88.2%

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

   if -2.4999999999999999e59 < t < 1.99999999999999992e-103

   1. Initial program 85.2%

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

   3. Simplified 86.1%

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

      1. associate-*r* 85.2%

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

      2. distribute-rgt-out-- 85.2%

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

      3. sub-neg 85.2%

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

      4. associate-*l* 90.1%

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

      5. *-commutative 90.1%

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

      6. *-commutative 90.1%

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

   6. Applied egg-rr 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-*r* 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l* 95.5%

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

      5. *-commutative 95.5%

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

      6. fma-neg 95.5%

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

      7. *-commutative 95.5%

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

      8. *-commutative 95.5%

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

      9. associate-*l* 95.5%

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

      10. *-commutative 95.5%

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

      11. distribute-rgt-neg-in 95.5%

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

      12. distribute-lft-neg-in 95.5%

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

      13. metadata-eval 95.5%

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

   8. Simplified 95.5%

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

      1. fma-undefine 95.5%

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

      2. associate-*l* 95.4%

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

      3. *-commutative 95.4%

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

   10. Applied egg-rr 95.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+59} \lor \neg \left(t \leq 2 \cdot 10^{-103}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+165}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-282}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* i (* x -4.0))))
        (t_2 (- (* b c) (* 27.0 (* j k))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.7e+165)
     t_3
     (if (<= t -1.65e+43)
       (* b (+ c (* -27.0 (/ (* j k) b))))
       (if (<= t -2.35e+17)
         t_3
         (if (<= t -1.12e-8)
           t_2
           (if (<= t -8e-22)
             t_3
             (if (<= t -4.5e-74)
               t_1
               (if (<= t 3.8e-282)
                 t_2
                 (if (<= t 1.6e+52)
                   t_1
                   (if (<= t 2.7e+82)
                     (- (* b c) (* 4.0 (* t a)))
                     (if (<= t 7.9e+87) t_1 t_3))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (i * (x * -4.0));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.7e+165) {
		tmp = t_3;
	} else if (t <= -1.65e+43) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= -2.35e+17) {
		tmp = t_3;
	} else if (t <= -1.12e-8) {
		tmp = t_2;
	} else if (t <= -8e-22) {
		tmp = t_3;
	} else if (t <= -4.5e-74) {
		tmp = t_1;
	} else if (t <= 3.8e-282) {
		tmp = t_2;
	} else if (t <= 1.6e+52) {
		tmp = t_1;
	} else if (t <= 2.7e+82) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (t <= 7.9e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    t_2 = (b * c) - (27.0d0 * (j * k))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.7d+165)) then
        tmp = t_3
    else if (t <= (-1.65d+43)) then
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    else if (t <= (-2.35d+17)) then
        tmp = t_3
    else if (t <= (-1.12d-8)) then
        tmp = t_2
    else if (t <= (-8d-22)) then
        tmp = t_3
    else if (t <= (-4.5d-74)) then
        tmp = t_1
    else if (t <= 3.8d-282) then
        tmp = t_2
    else if (t <= 1.6d+52) then
        tmp = t_1
    else if (t <= 2.7d+82) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (t <= 7.9d+87) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (i * (x * -4.0));
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.7e+165) {
		tmp = t_3;
	} else if (t <= -1.65e+43) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= -2.35e+17) {
		tmp = t_3;
	} else if (t <= -1.12e-8) {
		tmp = t_2;
	} else if (t <= -8e-22) {
		tmp = t_3;
	} else if (t <= -4.5e-74) {
		tmp = t_1;
	} else if (t <= 3.8e-282) {
		tmp = t_2;
	} else if (t <= 1.6e+52) {
		tmp = t_1;
	} else if (t <= 2.7e+82) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (t <= 7.9e+87) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (i * (x * -4.0))
	t_2 = (b * c) - (27.0 * (j * k))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.7e+165:
		tmp = t_3
	elif t <= -1.65e+43:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	elif t <= -2.35e+17:
		tmp = t_3
	elif t <= -1.12e-8:
		tmp = t_2
	elif t <= -8e-22:
		tmp = t_3
	elif t <= -4.5e-74:
		tmp = t_1
	elif t <= 3.8e-282:
		tmp = t_2
	elif t <= 1.6e+52:
		tmp = t_1
	elif t <= 2.7e+82:
		tmp = (b * c) - (4.0 * (t * a))
	elif t <= 7.9e+87:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.7e+165)
		tmp = t_3;
	elseif (t <= -1.65e+43)
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	elseif (t <= -2.35e+17)
		tmp = t_3;
	elseif (t <= -1.12e-8)
		tmp = t_2;
	elseif (t <= -8e-22)
		tmp = t_3;
	elseif (t <= -4.5e-74)
		tmp = t_1;
	elseif (t <= 3.8e-282)
		tmp = t_2;
	elseif (t <= 1.6e+52)
		tmp = t_1;
	elseif (t <= 2.7e+82)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (t <= 7.9e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (i * (x * -4.0));
	t_2 = (b * c) - (27.0 * (j * k));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.7e+165)
		tmp = t_3;
	elseif (t <= -1.65e+43)
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	elseif (t <= -2.35e+17)
		tmp = t_3;
	elseif (t <= -1.12e-8)
		tmp = t_2;
	elseif (t <= -8e-22)
		tmp = t_3;
	elseif (t <= -4.5e-74)
		tmp = t_1;
	elseif (t <= 3.8e-282)
		tmp = t_2;
	elseif (t <= 1.6e+52)
		tmp = t_1;
	elseif (t <= 2.7e+82)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (t <= 7.9e+87)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+165], t$95$3, If[LessEqual[t, -1.65e+43], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.35e+17], t$95$3, If[LessEqual[t, -1.12e-8], t$95$2, If[LessEqual[t, -8e-22], t$95$3, If[LessEqual[t, -4.5e-74], t$95$1, If[LessEqual[t, 3.8e-282], t$95$2, If[LessEqual[t, 1.6e+52], t$95$1, If[LessEqual[t, 2.7e+82], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.9e+87], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.70000000000000005e165 or -1.6500000000000001e43 < t < -2.35e17 or -1.11999999999999994e-8 < t < -8.0000000000000004e-22 or 7.8999999999999996e87 < 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 90.8%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -1.70000000000000005e165 < t < -1.6500000000000001e43

   1. Initial program 75.7%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around inf 53.1%

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

   6. Taylor expanded in b around inf 59.8%

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

   if -2.35e17 < t < -1.11999999999999994e-8 or -4.4999999999999999e-74 < t < 3.79999999999999992e-282

   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 82.5%

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

   4. Taylor expanded in a around 0 78.6%

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

   if -8.0000000000000004e-22 < t < -4.4999999999999999e-74 or 3.79999999999999992e-282 < t < 1.6e52 or 2.6999999999999999e82 < t < 7.8999999999999996e87

   1. Initial program 78.1%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in i around inf 66.2%

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

      1. metadata-eval 66.2%

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

      2. distribute-lft-neg-in 66.2%

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

      3. *-commutative 66.2%

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

      4. associate-*r* 66.2%

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

      5. distribute-rgt-neg-in 66.2%

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

      6. distribute-rgt-neg-in 66.2%

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

      7. metadata-eval 66.2%

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

      8. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if 1.6e52 < t < 2.6999999999999999e82

   1. Initial program 60.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in j around 0 100.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-8}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-282}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.08 \cdot 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.85 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{+219}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+278}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= (* b c) -1.05e+119)
     (* b c)
     (if (<= (* b c) -1.08e-252)
       t_1
       (if (<= (* b c) 0.0)
         (* t (* a -4.0))
         (if (<= (* b c) 2.85e-120)
           t_1
           (if (<= (* b c) 4.1e-13)
             (* -4.0 (* x i))
             (if (<= (* b c) 3.8e+219)
               (* -27.0 (* j k))
               (if (<= (* b c) 8.5e+278)
                 (* 18.0 (* t (* x (* y z))))
                 (* 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 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -1.05e+119) {
		tmp = b * c;
	} else if ((b * c) <= -1.08e-252) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2.85e-120) {
		tmp = t_1;
	} else if ((b * c) <= 4.1e-13) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.8e+219) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+278) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if ((b * c) <= (-1.05d+119)) then
        tmp = b * c
    else if ((b * c) <= (-1.08d-252)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 2.85d-120) then
        tmp = t_1
    else if ((b * c) <= 4.1d-13) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 3.8d+219) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 8.5d+278) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -1.05e+119) {
		tmp = b * c;
	} else if ((b * c) <= -1.08e-252) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2.85e-120) {
		tmp = t_1;
	} else if ((b * c) <= 4.1e-13) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.8e+219) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+278) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if (b * c) <= -1.05e+119:
		tmp = b * c
	elif (b * c) <= -1.08e-252:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 2.85e-120:
		tmp = t_1
	elif (b * c) <= 4.1e-13:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 3.8e+219:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 8.5e+278:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.05e+119)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.08e-252)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 2.85e-120)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.1e-13)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 3.8e+219)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 8.5e+278)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.05e+119)
		tmp = b * c;
	elseif ((b * c) <= -1.08e-252)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 2.85e-120)
		tmp = t_1;
	elseif ((b * c) <= 4.1e-13)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 3.8e+219)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 8.5e+278)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e+119], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.08e-252], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.85e-120], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.1e-13], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e+219], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.5e+278], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.04999999999999991e119 or 8.49999999999999993e278 < (*.f64 b c)

   1. Initial program 77.0%

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

   3. Simplified 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. associate-*r* 77.1%

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

   6. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. *-commutative 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in b around inf 65.0%

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

   if -1.04999999999999991e119 < (*.f64 b c) < -1.08e-252 or -0.0 < (*.f64 b c) < 2.85000000000000015e-120

   1. Initial program 83.2%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in j around inf 37.8%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

      3. metadata-eval 37.8%

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

      4. distribute-rgt-neg-in 37.8%

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

      5. *-commutative 37.8%

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

      6. distribute-rgt-neg-in 37.8%

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

      7. metadata-eval 37.8%

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

      8. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if -1.08e-252 < (*.f64 b c) < -0.0

   1. Initial program 88.6%

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

   3. Simplified 96.8%

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

      1. pow1 96.8%

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

      2. associate-*l* 96.9%

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

      3. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

      1. unpow1 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in a around inf 36.8%

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

       1. metadata-eval 36.8%

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

       2. distribute-lft-neg-in 36.8%

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

       3. associate-*r* 36.8%

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

       4. *-commutative 36.8%

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

       5. distribute-rgt-neg-in 36.8%

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

       6. distribute-lft-neg-in 36.8%

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

       7. metadata-eval 36.8%

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

       8. *-commutative 36.8%

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

   11. Simplified 36.8%

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

   if 2.85000000000000015e-120 < (*.f64 b c) < 4.1000000000000002e-13

   1. Initial program 75.6%

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

   3. Simplified 81.7%

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

      1. pow1 81.7%

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

      2. associate-*l* 81.7%

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

      3. associate-*r* 81.7%

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

   6. Applied egg-rr 81.7%

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

      1. unpow1 81.7%

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

      2. *-commutative 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in i around inf 45.8%

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

       1. *-commutative 45.8%

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

       2. *-commutative 45.8%

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

   11. Simplified 45.8%

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

   if 4.1000000000000002e-13 < (*.f64 b c) < 3.79999999999999996e219

   1. Initial program 87.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in j around inf 35.8%

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

   if 3.79999999999999996e219 < (*.f64 b c) < 8.49999999999999993e278

   1. Initial program 92.3%

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

   3. Simplified 92.3%

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

      1. pow1 92.3%

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

      2. associate-*l* 92.3%

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

      3. associate-*r* 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. unpow1 92.3%

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

      2. *-commutative 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around inf 59.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.08 \cdot 10^{-252}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.85 \cdot 10^{-120}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{+219}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+278}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 34.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+121}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+217}:\\ \;\;\;\;b \cdot \left(-27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+279}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= (* b c) -1e+121)
     (* b c)
     (if (<= (* b c) -2e-244)
       t_1
       (if (<= (* b c) 0.0)
         (* t (* a -4.0))
         (if (<= (* b c) 5e-121)
           t_1
           (if (<= (* b c) 5e-13)
             (* -4.0 (* x i))
             (if (<= (* b c) 2e+217)
               (* b (* -27.0 (/ (* j k) b)))
               (if (<= (* b c) 1e+279)
                 (* 18.0 (* t (* x (* y z))))
                 (* 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 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -1e+121) {
		tmp = b * c;
	} else if ((b * c) <= -2e-244) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 5e-121) {
		tmp = t_1;
	} else if ((b * c) <= 5e-13) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 2e+217) {
		tmp = b * (-27.0 * ((j * k) / b));
	} else if ((b * c) <= 1e+279) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if ((b * c) <= (-1d+121)) then
        tmp = b * c
    else if ((b * c) <= (-2d-244)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 5d-121) then
        tmp = t_1
    else if ((b * c) <= 5d-13) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 2d+217) then
        tmp = b * ((-27.0d0) * ((j * k) / b))
    else if ((b * c) <= 1d+279) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -1e+121) {
		tmp = b * c;
	} else if ((b * c) <= -2e-244) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 5e-121) {
		tmp = t_1;
	} else if ((b * c) <= 5e-13) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 2e+217) {
		tmp = b * (-27.0 * ((j * k) / b));
	} else if ((b * c) <= 1e+279) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if (b * c) <= -1e+121:
		tmp = b * c
	elif (b * c) <= -2e-244:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 5e-121:
		tmp = t_1
	elif (b * c) <= 5e-13:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 2e+217:
		tmp = b * (-27.0 * ((j * k) / b))
	elif (b * c) <= 1e+279:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1e+121)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2e-244)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 5e-121)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-13)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 2e+217)
		tmp = Float64(b * Float64(-27.0 * Float64(Float64(j * k) / b)));
	elseif (Float64(b * c) <= 1e+279)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1e+121)
		tmp = b * c;
	elseif ((b * c) <= -2e-244)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 5e-121)
		tmp = t_1;
	elseif ((b * c) <= 5e-13)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 2e+217)
		tmp = b * (-27.0 * ((j * k) / b));
	elseif ((b * c) <= 1e+279)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+121], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-244], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e-121], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-13], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+217], N[(b * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+279], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.00000000000000004e121 or 1.00000000000000006e279 < (*.f64 b c)

   1. Initial program 77.0%

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

   3. Simplified 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. associate-*r* 77.1%

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

   6. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. *-commutative 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in b around inf 65.0%

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

   if -1.00000000000000004e121 < (*.f64 b c) < -1.9999999999999999e-244 or -0.0 < (*.f64 b c) < 4.99999999999999989e-121

   1. Initial program 83.2%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in j around inf 37.8%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

      3. metadata-eval 37.8%

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

      4. distribute-rgt-neg-in 37.8%

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

      5. *-commutative 37.8%

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

      6. distribute-rgt-neg-in 37.8%

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

      7. metadata-eval 37.8%

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

      8. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if -1.9999999999999999e-244 < (*.f64 b c) < -0.0

   1. Initial program 88.6%

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

   3. Simplified 96.8%

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

      1. pow1 96.8%

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

      2. associate-*l* 96.9%

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

      3. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

      1. unpow1 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in a around inf 36.8%

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

       1. metadata-eval 36.8%

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

       2. distribute-lft-neg-in 36.8%

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

       3. associate-*r* 36.8%

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

       4. *-commutative 36.8%

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

       5. distribute-rgt-neg-in 36.8%

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

       6. distribute-lft-neg-in 36.8%

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

       7. metadata-eval 36.8%

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

       8. *-commutative 36.8%

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

   11. Simplified 36.8%

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

   if 4.99999999999999989e-121 < (*.f64 b c) < 4.9999999999999999e-13

   1. Initial program 75.6%

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

   3. Simplified 81.7%

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

      1. pow1 81.7%

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

      2. associate-*l* 81.7%

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

      3. associate-*r* 81.7%

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

   6. Applied egg-rr 81.7%

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

      1. unpow1 81.7%

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

      2. *-commutative 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in i around inf 45.8%

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

       1. *-commutative 45.8%

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

       2. *-commutative 45.8%

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

   11. Simplified 45.8%

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

   if 4.9999999999999999e-13 < (*.f64 b c) < 1.99999999999999992e217

   1. Initial program 87.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in b around inf 54.0%

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

   6. Taylor expanded in b around inf 53.8%

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

   7. Taylor expanded in c around 0 35.7%

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

   if 1.99999999999999992e217 < (*.f64 b c) < 1.00000000000000006e279

   1. Initial program 92.3%

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

   3. Simplified 92.3%

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

      1. pow1 92.3%

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

      2. associate-*l* 92.3%

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

      3. associate-*r* 92.3%

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

   6. Applied egg-rr 92.3%

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

      1. unpow1 92.3%

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

      2. *-commutative 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around inf 59.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+121}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-244}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-121}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+217}:\\ \;\;\;\;b \cdot \left(-27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+279}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_3 \leq -1.5 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 0.0001:\\ \;\;\;\;t\_2 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* i (- (/ (* b c) i) (+ (* x 4.0) (* 27.0 (/ (* j k) i))))))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
        (t_3 (* k (* j 27.0))))
   (if (<= t_3 -1.5e+137)
     t_1
     (if (<= t_3 0.0001)
       (- t_2 (* 4.0 (* x i)))
       (if (<= t_3 2e+64)
         t_1
         (if (<= t_3 1e+154) t_2 (- (- (* b c) (* 4.0 (* t a))) t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1.5e+137) {
		tmp = t_1;
	} else if (t_3 <= 0.0001) {
		tmp = t_2 - (4.0 * (x * i));
	} else if (t_3 <= 2e+64) {
		tmp = t_1;
	} else if (t_3 <= 1e+154) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (((b * c) / i) - ((x * 4.0d0) + (27.0d0 * ((j * k) / i))))
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    t_3 = k * (j * 27.0d0)
    if (t_3 <= (-1.5d+137)) then
        tmp = t_1
    else if (t_3 <= 0.0001d0) then
        tmp = t_2 - (4.0d0 * (x * i))
    else if (t_3 <= 2d+64) then
        tmp = t_1
    else if (t_3 <= 1d+154) then
        tmp = t_2
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1.5e+137) {
		tmp = t_1;
	} else if (t_3 <= 0.0001) {
		tmp = t_2 - (4.0 * (x * i));
	} else if (t_3 <= 2e+64) {
		tmp = t_1;
	} else if (t_3 <= 1e+154) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))))
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	t_3 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -1.5e+137:
		tmp = t_1
	elif t_3 <= 0.0001:
		tmp = t_2 - (4.0 * (x * i))
	elif t_3 <= 2e+64:
		tmp = t_1
	elif t_3 <= 1e+154:
		tmp = t_2
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(Float64(Float64(b * c) / i) - Float64(Float64(x * 4.0) + Float64(27.0 * Float64(Float64(j * k) / i)))))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -1.5e+137)
		tmp = t_1;
	elseif (t_3 <= 0.0001)
		tmp = Float64(t_2 - Float64(4.0 * Float64(x * i)));
	elseif (t_3 <= 2e+64)
		tmp = t_1;
	elseif (t_3 <= 1e+154)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_3);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -1.5e+137)
		tmp = t_1;
	elseif (t_3 <= 0.0001)
		tmp = t_2 - (4.0 * (x * i));
	elseif (t_3 <= 2e+64)
		tmp = t_1;
	elseif (t_3 <= 1e+154)
		tmp = t_2;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * N[(N[(N[(b * c), $MachinePrecision] / i), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1.5e+137], t$95$1, If[LessEqual[t$95$3, 0.0001], N[(t$95$2 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+64], t$95$1, If[LessEqual[t$95$3, 1e+154], t$95$2, N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.5e137 or 1.00000000000000005e-4 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000004e64

   1. Initial program 79.2%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in i around inf 83.1%

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

   6. Taylor expanded in t around 0 86.8%

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

   if -1.5e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000005e-4

   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 90.5%

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

   5. Taylor expanded in j around 0 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 2.00000000000000004e64 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e154

   1. Initial program 74.7%

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

   3. Simplified 87.5%

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

      1. pow1 87.5%

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

      2. associate-*l* 87.5%

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

      3. associate-*r* 87.5%

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

   6. Applied egg-rr 87.5%

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

      1. unpow1 87.5%

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

      2. *-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in i around 0 87.5%

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

   10. Taylor expanded in j around 0 77.8%

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

   if 1.00000000000000004e154 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1.5 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 0.0001:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+154}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1.5 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+47}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - \left(4 \cdot \frac{t \cdot a}{b} + 27 \cdot \frac{j \cdot k}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
        (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1.5e+137)
     (* i (- (/ (* b c) i) (+ (* x 4.0) (* 27.0 (/ (* j k) i)))))
     (if (<= t_2 5e+47)
       (- t_1 (* 4.0 (* x i)))
       (if (<= t_2 5e+304)
         (- t_1 (* 27.0 (* j k)))
         (* b (- c (+ (* 4.0 (/ (* t a) b)) (* 27.0 (/ (* j k) b))))))))))

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) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1.5e+137) {
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	} else if (t_2 <= 5e+47) {
		tmp = t_1 - (4.0 * (x * i));
	} else if (t_2 <= 5e+304) {
		tmp = t_1 - (27.0 * (j * k));
	} else {
		tmp = b * (c - ((4.0 * ((t * a) / b)) + (27.0 * ((j * k) / b))));
	}
	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) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1.5d+137)) then
        tmp = i * (((b * c) / i) - ((x * 4.0d0) + (27.0d0 * ((j * k) / i))))
    else if (t_2 <= 5d+47) then
        tmp = t_1 - (4.0d0 * (x * i))
    else if (t_2 <= 5d+304) then
        tmp = t_1 - (27.0d0 * (j * k))
    else
        tmp = b * (c - ((4.0d0 * ((t * a) / b)) + (27.0d0 * ((j * k) / b))))
    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) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1.5e+137) {
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	} else if (t_2 <= 5e+47) {
		tmp = t_1 - (4.0 * (x * i));
	} else if (t_2 <= 5e+304) {
		tmp = t_1 - (27.0 * (j * k));
	} else {
		tmp = b * (c - ((4.0 * ((t * a) / b)) + (27.0 * ((j * k) / b))));
	}
	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) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1.5e+137:
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))))
	elif t_2 <= 5e+47:
		tmp = t_1 - (4.0 * (x * i))
	elif t_2 <= 5e+304:
		tmp = t_1 - (27.0 * (j * k))
	else:
		tmp = b * (c - ((4.0 * ((t * a) / b)) + (27.0 * ((j * k) / b))))
	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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1.5e+137)
		tmp = Float64(i * Float64(Float64(Float64(b * c) / i) - Float64(Float64(x * 4.0) + Float64(27.0 * Float64(Float64(j * k) / i)))));
	elseif (t_2 <= 5e+47)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 5e+304)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(b * Float64(c - Float64(Float64(4.0 * Float64(Float64(t * a) / b)) + Float64(27.0 * Float64(Float64(j * k) / b)))));
	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) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1.5e+137)
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	elseif (t_2 <= 5e+47)
		tmp = t_1 - (4.0 * (x * i));
	elseif (t_2 <= 5e+304)
		tmp = t_1 - (27.0 * (j * k));
	else
		tmp = b * (c - ((4.0 * ((t * a) / b)) + (27.0 * ((j * k) / b))));
	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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1.5e+137], N[(i * N[(N[(N[(b * c), $MachinePrecision] / i), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+47], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c - N[(N[(4.0 * N[(N[(t * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.5e137

   1. Initial program 77.2%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in i around inf 84.0%

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

   6. Taylor expanded in t around 0 86.4%

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

   if -1.5e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000022e47

   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 89.6%

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

   5. Taylor expanded in j around 0 84.1%

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

   if 5.00000000000000022e47 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e304

   1. Initial program 91.1%

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

   3. Simplified 93.3%

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

      1. pow1 93.3%

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

      2. associate-*l* 93.3%

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

      3. associate-*r* 93.3%

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

   6. Applied egg-rr 93.3%

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

      1. unpow1 93.3%

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

      2. *-commutative 93.3%

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

   8. Simplified 93.3%

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

   9. Taylor expanded in i around 0 93.3%

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

   if 4.9999999999999997e304 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 47.1%

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

   3. Taylor expanded in x around 0 52.9%

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

   4. Taylor expanded in b around -inf 70.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot c + \left(4 \cdot \frac{a \cdot t}{b} + 27 \cdot \frac{j \cdot k}{b}\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1.5 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - \left(4 \cdot \frac{t \cdot a}{b} + 27 \cdot \frac{j \cdot k}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.05 \cdot 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+232}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= (* b c) -2.4e+116)
     (* b c)
     (if (<= (* b c) -2.05e-252)
       t_1
       (if (<= (* b c) 0.0)
         (* t (* a -4.0))
         (if (<= (* b c) 4.2e-121)
           t_1
           (if (<= (* b c) 2.25e-11)
             (* -4.0 (* x i))
             (if (<= (* b c) 3e+232) (* -27.0 (* j k)) (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -2.4e+116) {
		tmp = b * c;
	} else if ((b * c) <= -2.05e-252) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 4.2e-121) {
		tmp = t_1;
	} else if ((b * c) <= 2.25e-11) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3e+232) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if ((b * c) <= (-2.4d+116)) then
        tmp = b * c
    else if ((b * c) <= (-2.05d-252)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 4.2d-121) then
        tmp = t_1
    else if ((b * c) <= 2.25d-11) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 3d+232) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -2.4e+116) {
		tmp = b * c;
	} else if ((b * c) <= -2.05e-252) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 4.2e-121) {
		tmp = t_1;
	} else if ((b * c) <= 2.25e-11) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3e+232) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if (b * c) <= -2.4e+116:
		tmp = b * c
	elif (b * c) <= -2.05e-252:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 4.2e-121:
		tmp = t_1
	elif (b * c) <= 2.25e-11:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 3e+232:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.4e+116)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.05e-252)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 4.2e-121)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.25e-11)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 3e+232)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if ((b * c) <= -2.4e+116)
		tmp = b * c;
	elseif ((b * c) <= -2.05e-252)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 4.2e-121)
		tmp = t_1;
	elseif ((b * c) <= 2.25e-11)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 3e+232)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+116], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.05e-252], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e-121], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.25e-11], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e+232], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.4e116 or 3.00000000000000003e232 < (*.f64 b c)

   1. Initial program 79.3%

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

   3. Simplified 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. Step-by-step derivation

      1. pow1 79.3%

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

      2. associate-*l* 79.3%

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

      3. associate-*r* 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow1 79.3%

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

      2. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in b around inf 58.8%

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

   if -2.4e116 < (*.f64 b c) < -2.05000000000000007e-252 or -0.0 < (*.f64 b c) < 4.1999999999999997e-121

   1. Initial program 83.2%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in j around inf 37.8%

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

      1. associate-*r* 37.8%

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

      2. *-commutative 37.8%

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

      3. metadata-eval 37.8%

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

      4. distribute-rgt-neg-in 37.8%

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

      5. *-commutative 37.8%

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

      6. distribute-rgt-neg-in 37.8%

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

      7. metadata-eval 37.8%

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

      8. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if -2.05000000000000007e-252 < (*.f64 b c) < -0.0

   1. Initial program 88.6%

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

   3. Simplified 96.8%

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

      1. pow1 96.8%

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

      2. associate-*l* 96.9%

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

      3. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

      1. unpow1 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in a around inf 36.8%

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

       1. metadata-eval 36.8%

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

       2. distribute-lft-neg-in 36.8%

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

       3. associate-*r* 36.8%

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

       4. *-commutative 36.8%

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

       5. distribute-rgt-neg-in 36.8%

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

       6. distribute-lft-neg-in 36.8%

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

       7. metadata-eval 36.8%

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

       8. *-commutative 36.8%

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

   11. Simplified 36.8%

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

   if 4.1999999999999997e-121 < (*.f64 b c) < 2.25e-11

   1. Initial program 75.6%

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

   3. Simplified 81.7%

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

      1. pow1 81.7%

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

      2. associate-*l* 81.7%

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

      3. associate-*r* 81.7%

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

   6. Applied egg-rr 81.7%

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

      1. unpow1 81.7%

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

      2. *-commutative 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in i around inf 45.8%

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

       1. *-commutative 45.8%

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

       2. *-commutative 45.8%

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

   11. Simplified 45.8%

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

   if 2.25e-11 < (*.f64 b c) < 3.00000000000000003e232

   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 90.3%

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

   5. Taylor expanded in j around inf 34.9%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.05 \cdot 10^{-252}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{-121}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+232}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+24} \lor \neg \left(x \leq 5.5 \cdot 10^{+111}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))
   (if (<= x -1.2e+33)
     t_2
     (if (<= x -2.4e-82)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 2.8e-193)
         (+ t_1 (* a (* t -4.0)))
         (if (<= x 3.7e-26)
           (+ t_1 (* b c))
           (if (or (<= x 8.5e+24) (not (<= x 5.5e+111)))
             t_2
             (* b (+ c (* -27.0 (/ (* j k) b)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.2e+33) {
		tmp = t_2;
	} else if (x <= -2.4e-82) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.8e-193) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (x <= 3.7e-26) {
		tmp = t_1 + (b * c);
	} else if ((x <= 8.5e+24) || !(x <= 5.5e+111)) {
		tmp = t_2;
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    if (x <= (-1.2d+33)) then
        tmp = t_2
    else if (x <= (-2.4d-82)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 2.8d-193) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (x <= 3.7d-26) then
        tmp = t_1 + (b * c)
    else if ((x <= 8.5d+24) .or. (.not. (x <= 5.5d+111))) then
        tmp = t_2
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.2e+33) {
		tmp = t_2;
	} else if (x <= -2.4e-82) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.8e-193) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (x <= 3.7e-26) {
		tmp = t_1 + (b * c);
	} else if ((x <= 8.5e+24) || !(x <= 5.5e+111)) {
		tmp = t_2;
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	tmp = 0
	if x <= -1.2e+33:
		tmp = t_2
	elif x <= -2.4e-82:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 2.8e-193:
		tmp = t_1 + (a * (t * -4.0))
	elif x <= 3.7e-26:
		tmp = t_1 + (b * c)
	elif (x <= 8.5e+24) or not (x <= 5.5e+111):
		tmp = t_2
	else:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -1.2e+33)
		tmp = t_2;
	elseif (x <= -2.4e-82)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 2.8e-193)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (x <= 3.7e-26)
		tmp = Float64(t_1 + Float64(b * c));
	elseif ((x <= 8.5e+24) || !(x <= 5.5e+111))
		tmp = t_2;
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -1.2e+33)
		tmp = t_2;
	elseif (x <= -2.4e-82)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 2.8e-193)
		tmp = t_1 + (a * (t * -4.0));
	elseif (x <= 3.7e-26)
		tmp = t_1 + (b * c);
	elseif ((x <= 8.5e+24) || ~((x <= 5.5e+111)))
		tmp = t_2;
	else
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+33], t$95$2, If[LessEqual[x, -2.4e-82], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-193], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-26], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.5e+24], N[Not[LessEqual[x, 5.5e+111]], $MachinePrecision]], t$95$2, N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.2e33 or 3.6999999999999999e-26 < x < 8.49999999999999959e24 or 5.4999999999999998e111 < x

   1. Initial program 70.5%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around inf 71.8%

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

   if -1.2e33 < x < -2.40000000000000008e-82

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in a around 0 74.4%

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

   if -2.40000000000000008e-82 < x < 2.8000000000000002e-193

   1. Initial program 91.1%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in a around inf 71.2%

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

      1. metadata-eval 71.2%

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

      2. distribute-lft-neg-in 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-*l* 71.2%

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

      5. distribute-lft-neg-in 71.2%

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

      6. distribute-lft-neg-in 71.2%

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

      7. metadata-eval 71.2%

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

   7. Simplified 71.2%

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

   if 2.8000000000000002e-193 < x < 3.6999999999999999e-26

   1. Initial program 97.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in b around inf 68.5%

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

   if 8.49999999999999959e24 < x < 5.4999999999999998e111

   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 93.3%

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

   5. Taylor expanded in b around inf 67.9%

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

   6. Taylor expanded in b around inf 74.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-82}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+24} \lor \neg \left(x \leq 5.5 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.16 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+24} \lor \neg \left(x \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

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))) (* k (* j 27.0))))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))
   (if (<= x -2.7e+249)
     t_2
     (if (<= x -5e+210)
       t_1
       (if (<= x -2.16e+33)
         t_2
         (if (<= x 8e-26)
           t_1
           (if (or (<= x 6.6e+24) (not (<= x 1.5e+113)))
             t_2
             (* b (+ c (* -27.0 (/ (* j k) b)))))))))))

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))) - (k * (j * 27.0));
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.7e+249) {
		tmp = t_2;
	} else if (x <= -5e+210) {
		tmp = t_1;
	} else if (x <= -2.16e+33) {
		tmp = t_2;
	} else if (x <= 8e-26) {
		tmp = t_1;
	} else if ((x <= 6.6e+24) || !(x <= 1.5e+113)) {
		tmp = t_2;
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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))) - (k * (j * 27.0d0))
    t_2 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    if (x <= (-2.7d+249)) then
        tmp = t_2
    else if (x <= (-5d+210)) then
        tmp = t_1
    else if (x <= (-2.16d+33)) then
        tmp = t_2
    else if (x <= 8d-26) then
        tmp = t_1
    else if ((x <= 6.6d+24) .or. (.not. (x <= 1.5d+113))) then
        tmp = t_2
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    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))) - (k * (j * 27.0));
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.7e+249) {
		tmp = t_2;
	} else if (x <= -5e+210) {
		tmp = t_1;
	} else if (x <= -2.16e+33) {
		tmp = t_2;
	} else if (x <= 8e-26) {
		tmp = t_1;
	} else if ((x <= 6.6e+24) || !(x <= 1.5e+113)) {
		tmp = t_2;
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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))) - (k * (j * 27.0))
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	tmp = 0
	if x <= -2.7e+249:
		tmp = t_2
	elif x <= -5e+210:
		tmp = t_1
	elif x <= -2.16e+33:
		tmp = t_2
	elif x <= 8e-26:
		tmp = t_1
	elif (x <= 6.6e+24) or not (x <= 1.5e+113):
		tmp = t_2
	else:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	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(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.7e+249)
		tmp = t_2;
	elseif (x <= -5e+210)
		tmp = t_1;
	elseif (x <= -2.16e+33)
		tmp = t_2;
	elseif (x <= 8e-26)
		tmp = t_1;
	elseif ((x <= 6.6e+24) || !(x <= 1.5e+113))
		tmp = t_2;
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	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))) - (k * (j * 27.0));
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.7e+249)
		tmp = t_2;
	elseif (x <= -5e+210)
		tmp = t_1;
	elseif (x <= -2.16e+33)
		tmp = t_2;
	elseif (x <= 8e-26)
		tmp = t_1;
	elseif ((x <= 6.6e+24) || ~((x <= 1.5e+113)))
		tmp = t_2;
	else
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	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[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+249], t$95$2, If[LessEqual[x, -5e+210], t$95$1, If[LessEqual[x, -2.16e+33], t$95$2, If[LessEqual[x, 8e-26], t$95$1, If[Or[LessEqual[x, 6.6e+24], N[Not[LessEqual[x, 1.5e+113]], $MachinePrecision]], t$95$2, N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.70000000000000018e249 or -4.9999999999999998e210 < x < -2.1600000000000001e33 or 8.0000000000000003e-26 < x < 6.5999999999999998e24 or 1.5e113 < x

   1. Initial program 73.1%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around inf 76.4%

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

   if -2.70000000000000018e249 < x < -4.9999999999999998e210 or -2.1600000000000001e33 < x < 8.0000000000000003e-26

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 6.5999999999999998e24 < x < 1.5e113

   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 93.3%

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

   5. Taylor expanded in b around inf 67.9%

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

   6. Taylor expanded in b around inf 74.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+210}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -2.16 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-26}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+24} \lor \neg \left(x \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+94} \lor \neg \left(t \leq 10^{+20}\right):\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - t\_1\\ \end{array} \end{array} \]

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 (* i 4.0)) (* j (* k 27.0)))))
   (if (or (<= t -1e+94) (not (<= t 1e+20)))
     (- (* t (- (+ (* 18.0 (* x (* y z))) (/ (* b c) t)) (* a 4.0))) t_1)
     (- (+ (+ (* y (* x (* 18.0 (* t z)))) (* a (* t -4.0))) (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (i * 4.0)) + (j * (k * 27.0));
	double tmp;
	if ((t <= -1e+94) || !(t <= 1e+20)) {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	} else {
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - 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 * (i * 4.0d0)) + (j * (k * 27.0d0))
    if ((t <= (-1d+94)) .or. (.not. (t <= 1d+20))) then
        tmp = (t * (((18.0d0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0d0))) - t_1
    else
        tmp = (((y * (x * (18.0d0 * (t * z)))) + (a * (t * (-4.0d0)))) + (b * c)) - 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 * (i * 4.0)) + (j * (k * 27.0));
	double tmp;
	if ((t <= -1e+94) || !(t <= 1e+20)) {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	} else {
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - 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 * (i * 4.0)) + (j * (k * 27.0))
	tmp = 0
	if (t <= -1e+94) or not (t <= 1e+20):
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1
	else:
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - 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(i * 4.0)) + Float64(j * Float64(k * 27.0)))
	tmp = 0.0
	if ((t <= -1e+94) || !(t <= 1e+20))
		tmp = Float64(Float64(t * Float64(Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t)) - Float64(a * 4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(y * Float64(x * Float64(18.0 * Float64(t * z)))) + Float64(a * Float64(t * -4.0))) + Float64(b * c)) - 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 * (i * 4.0)) + (j * (k * 27.0));
	tmp = 0.0;
	if ((t <= -1e+94) || ~((t <= 1e+20)))
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	else
		tmp = (((y * (x * (18.0 * (t * z)))) + (a * (t * -4.0))) + (b * c)) - 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[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -1e+94], N[Not[LessEqual[t, 1e+20]], $MachinePrecision]], N[(N[(t * N[(N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(y * N[(x * N[(18.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1e94 or 1e20 < t

   1. Initial program 82.6%

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

   3. Simplified 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

   5. Taylor expanded in t around inf 89.9%

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

   if -1e94 < t < 1e20

   1. Initial program 83.3%

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

   3. Simplified 83.9%

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

      1. associate-*r* 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-- 83.2%

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

      3. sub-neg 83.2%

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

      4. associate-*l* 87.0%

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

      5. *-commutative 87.0%

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

      6. *-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

      1. sub-neg 87.0%

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

      2. associate-*r* 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-*l* 92.4%

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

      5. *-commutative 92.4%

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

      6. fma-neg 92.4%

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

      7. *-commutative 92.4%

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

      8. *-commutative 92.4%

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

      9. associate-*l* 92.4%

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

      10. *-commutative 92.4%

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

      11. distribute-rgt-neg-in 92.4%

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

      12. distribute-lft-neg-in 92.4%

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

      13. metadata-eval 92.4%

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

   8. Simplified 92.4%

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

      1. fma-undefine 92.4%

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

      2. associate-*l* 92.4%

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

      3. *-commutative 92.4%

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

   10. Applied egg-rr 92.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+94} \lor \neg \left(t \leq 10^{+20}\right):\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot \left(18 \cdot \left(t \cdot z\right)\right)\right) + a \cdot \left(t \cdot -4\right)\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -13600:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+24} \lor \neg \left(x \leq 1.7 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -13600.0)
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (if (<= x 1.3e-25)
     (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))
     (if (or (<= x 7.2e+24) (not (<= x 1.7e+113)))
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
       (* i (- (/ (* b c) i) (+ (* x 4.0) (* 27.0 (/ (* j k) i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -13600.0) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 1.3e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if ((x <= 7.2e+24) || !(x <= 1.7e+113)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-13600.0d0)) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else if (x <= 1.3d-25) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else if ((x <= 7.2d+24) .or. (.not. (x <= 1.7d+113))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else
        tmp = i * (((b * c) / i) - ((x * 4.0d0) + (27.0d0 * ((j * k) / i))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -13600.0) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 1.3e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if ((x <= 7.2e+24) || !(x <= 1.7e+113)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -13600.0:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	elif x <= 1.3e-25:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	elif (x <= 7.2e+24) or not (x <= 1.7e+113):
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	else:
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -13600.0)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	elseif (x <= 1.3e-25)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif ((x <= 7.2e+24) || !(x <= 1.7e+113))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	else
		tmp = Float64(i * Float64(Float64(Float64(b * c) / i) - Float64(Float64(x * 4.0) + Float64(27.0 * Float64(Float64(j * k) / i)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -13600.0)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	elseif (x <= 1.3e-25)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	elseif ((x <= 7.2e+24) || ~((x <= 1.7e+113)))
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	else
		tmp = i * (((b * c) / i) - ((x * 4.0) + (27.0 * ((j * k) / i))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -13600.0], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-25], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 7.2e+24], N[Not[LessEqual[x, 1.7e+113]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(N[(b * c), $MachinePrecision] / i), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -13600

   1. Initial program 71.4%

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

   3. Simplified 80.4%

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

      1. pow1 80.4%

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

      2. associate-*l* 80.4%

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

      3. associate-*r* 80.4%

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

   6. Applied egg-rr 80.4%

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

      1. unpow1 80.4%

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

      2. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in i around 0 74.7%

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

   10. Taylor expanded in j around 0 70.4%

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

   if -13600 < x < 1.3e-25

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 80.8%

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

   if 1.3e-25 < x < 7.19999999999999966e24 or 1.70000000000000009e113 < x

   1. Initial program 72.1%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in x around inf 78.1%

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

   if 7.19999999999999966e24 < x < 1.70000000000000009e113

   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 93.3%

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

   5. Taylor expanded in i around inf 80.9%

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

   6. Taylor expanded in t around 0 80.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -13600:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+24} \lor \neg \left(x \leq 1.7 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\frac{b \cdot c}{i} - \left(x \cdot 4 + 27 \cdot \frac{j \cdot k}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-200}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-266}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* a (* t -4.0)))))
   (if (<= a -4.8e+42)
     t_2
     (if (<= a -9.2e-200)
       (+ t_1 (* b c))
       (if (<= a -2.7e-266)
         (* 18.0 (* t (* x (* y z))))
         (if (<= a 3.4e-61)
           (* b (+ c (* -27.0 (/ (* j k) b))))
           (if (<= a 4.4e+65) (+ t_1 (* i (* x -4.0))) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (a * (t * -4.0));
	double tmp;
	if (a <= -4.8e+42) {
		tmp = t_2;
	} else if (a <= -9.2e-200) {
		tmp = t_1 + (b * c);
	} else if (a <= -2.7e-266) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (a <= 3.4e-61) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (a <= 4.4e+65) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (a * (t * (-4.0d0)))
    if (a <= (-4.8d+42)) then
        tmp = t_2
    else if (a <= (-9.2d-200)) then
        tmp = t_1 + (b * c)
    else if (a <= (-2.7d-266)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (a <= 3.4d-61) then
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    else if (a <= 4.4d+65) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (a * (t * -4.0));
	double tmp;
	if (a <= -4.8e+42) {
		tmp = t_2;
	} else if (a <= -9.2e-200) {
		tmp = t_1 + (b * c);
	} else if (a <= -2.7e-266) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (a <= 3.4e-61) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (a <= 4.4e+65) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (a * (t * -4.0))
	tmp = 0
	if a <= -4.8e+42:
		tmp = t_2
	elif a <= -9.2e-200:
		tmp = t_1 + (b * c)
	elif a <= -2.7e-266:
		tmp = 18.0 * (t * (x * (y * z)))
	elif a <= 3.4e-61:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	elif a <= 4.4e+65:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(a * Float64(t * -4.0)))
	tmp = 0.0
	if (a <= -4.8e+42)
		tmp = t_2;
	elseif (a <= -9.2e-200)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (a <= -2.7e-266)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (a <= 3.4e-61)
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	elseif (a <= 4.4e+65)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (a * (t * -4.0));
	tmp = 0.0;
	if (a <= -4.8e+42)
		tmp = t_2;
	elseif (a <= -9.2e-200)
		tmp = t_1 + (b * c);
	elseif (a <= -2.7e-266)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (a <= 3.4e-61)
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	elseif (a <= 4.4e+65)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+42], t$95$2, If[LessEqual[a, -9.2e-200], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-266], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-61], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+65], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.7999999999999997e42 or 4.3999999999999997e65 < a

   1. Initial program 78.7%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 62.7%

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

      1. metadata-eval 62.7%

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

      2. distribute-lft-neg-in 62.7%

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

      3. *-commutative 62.7%

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

      4. associate-*l* 62.7%

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

      5. distribute-lft-neg-in 62.7%

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

      6. distribute-lft-neg-in 62.7%

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

      7. metadata-eval 62.7%

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

   7. Simplified 62.7%

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

   if -4.7999999999999997e42 < a < -9.2000000000000003e-200

   1. Initial program 89.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in b around inf 68.2%

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

   if -9.2000000000000003e-200 < a < -2.69999999999999996e-266

   1. Initial program 93.8%

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

   3. Simplified 93.5%

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

      1. pow1 93.5%

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

      2. associate-*l* 93.7%

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

      3. associate-*r* 93.7%

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

   6. Applied egg-rr 93.7%

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

      1. unpow1 93.7%

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

      2. *-commutative 93.7%

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

   8. Simplified 93.7%

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

   9. Taylor expanded in z around inf 57.5%

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

   if -2.69999999999999996e-266 < a < 3.3999999999999998e-61

   1. Initial program 81.1%

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

   3. Simplified 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 b around inf 57.1%

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

   6. Taylor expanded in b around inf 62.5%

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

   if 3.3999999999999998e-61 < a < 4.3999999999999997e65

   1. Initial program 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in i around inf 65.2%

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

      1. metadata-eval 65.2%

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

      2. distribute-lft-neg-in 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*r* 65.2%

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

      5. distribute-rgt-neg-in 65.2%

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

      6. distribute-rgt-neg-in 65.2%

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

      7. metadata-eval 65.2%

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

      8. *-commutative 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-200}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-266}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) 5e+293)
   (-
    (+ (* b c) (* t (- (* x (* z (* 18.0 y))) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (* b (+ c (* -27.0 (/ (* j k) b))))))

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+293) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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+293) then
        tmp = ((b * c) + (t * ((x * (z * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    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+293) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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+293:
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	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+293)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	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+293)
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 5e+293], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 5.00000000000000033e293

   1. Initial program 85.4%

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

   3. Simplified 88.3%

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

      1. pow1 88.3%

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

      2. associate-*l* 88.3%

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

      3. associate-*r* 88.3%

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

   6. Applied egg-rr 88.3%

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

      1. unpow1 88.3%

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

      2. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if 5.00000000000000033e293 < (*.f64 b c)

   1. Initial program 52.6%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in b around inf 74.3%

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

   6. Taylor expanded in b around inf 90.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_3 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+215}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)) (* b c)))
        (t_2 (- (* b c) (* 4.0 (* t a))))
        (t_3 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -2.25e+215)
     t_3
     (if (<= t -1.05e+163)
       t_2
       (if (<= t -2.5e+42)
         t_1
         (if (<= t -8.2e+18) t_3 (if (<= t 9.5e+36) 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)) + (b * c);
	double t_2 = (b * c) - (4.0 * (t * a));
	double t_3 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -2.25e+215) {
		tmp = t_3;
	} else if (t <= -1.05e+163) {
		tmp = t_2;
	} else if (t <= -2.5e+42) {
		tmp = t_1;
	} else if (t <= -8.2e+18) {
		tmp = t_3;
	} else if (t <= 9.5e+36) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = (b * c) - (4.0d0 * (t * a))
    t_3 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-2.25d+215)) then
        tmp = t_3
    else if (t <= (-1.05d+163)) then
        tmp = t_2
    else if (t <= (-2.5d+42)) then
        tmp = t_1
    else if (t <= (-8.2d+18)) then
        tmp = t_3
    else if (t <= 9.5d+36) 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 = (j * (k * -27.0)) + (b * c);
	double t_2 = (b * c) - (4.0 * (t * a));
	double t_3 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -2.25e+215) {
		tmp = t_3;
	} else if (t <= -1.05e+163) {
		tmp = t_2;
	} else if (t <= -2.5e+42) {
		tmp = t_1;
	} else if (t <= -8.2e+18) {
		tmp = t_3;
	} else if (t <= 9.5e+36) {
		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 = (j * (k * -27.0)) + (b * c)
	t_2 = (b * c) - (4.0 * (t * a))
	t_3 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -2.25e+215:
		tmp = t_3
	elif t <= -1.05e+163:
		tmp = t_2
	elif t <= -2.5e+42:
		tmp = t_1
	elif t <= -8.2e+18:
		tmp = t_3
	elif t <= 9.5e+36:
		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(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	t_3 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -2.25e+215)
		tmp = t_3;
	elseif (t <= -1.05e+163)
		tmp = t_2;
	elseif (t <= -2.5e+42)
		tmp = t_1;
	elseif (t <= -8.2e+18)
		tmp = t_3;
	elseif (t <= 9.5e+36)
		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 = (j * (k * -27.0)) + (b * c);
	t_2 = (b * c) - (4.0 * (t * a));
	t_3 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -2.25e+215)
		tmp = t_3;
	elseif (t <= -1.05e+163)
		tmp = t_2;
	elseif (t <= -2.5e+42)
		tmp = t_1;
	elseif (t <= -8.2e+18)
		tmp = t_3;
	elseif (t <= 9.5e+36)
		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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+215], t$95$3, If[LessEqual[t, -1.05e+163], t$95$2, If[LessEqual[t, -2.5e+42], t$95$1, If[LessEqual[t, -8.2e+18], t$95$3, If[LessEqual[t, 9.5e+36], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2500000000000001e215 or -2.50000000000000003e42 < t < -8.2e18

   1. Initial program 87.8%

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

   3. Simplified 93.8%

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

      1. pow1 93.8%

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

      2. associate-*l* 93.9%

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

      3. associate-*r* 93.8%

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

   6. Applied egg-rr 93.8%

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

      1. unpow1 93.8%

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

      2. *-commutative 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in z around inf 67.1%

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

   if -2.2500000000000001e215 < t < -1.05e163 or 9.49999999999999974e36 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0 69.5%

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

   4. Taylor expanded in j around 0 59.2%

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

   if -1.05e163 < t < -2.50000000000000003e42 or -8.2e18 < t < 9.49999999999999974e36

   1. Initial program 81.5%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in b around inf 57.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+215}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+163}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (* 4.0 (* t a)))) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -3.4e+216)
     t_2
     (if (<= t -2.35e+163)
       t_1
       (if (<= t -2e+43)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= t -6.6e+17)
           t_2
           (if (<= t 5.1e+36) (+ (* j (* k -27.0)) (* b c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -3.4e+216) {
		tmp = t_2;
	} else if (t <= -2.35e+163) {
		tmp = t_1;
	} else if (t <= -2e+43) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= -6.6e+17) {
		tmp = t_2;
	} else if (t <= 5.1e+36) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (t * a))
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-3.4d+216)) then
        tmp = t_2
    else if (t <= (-2.35d+163)) then
        tmp = t_1
    else if (t <= (-2d+43)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= (-6.6d+17)) then
        tmp = t_2
    else if (t <= 5.1d+36) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -3.4e+216) {
		tmp = t_2;
	} else if (t <= -2.35e+163) {
		tmp = t_1;
	} else if (t <= -2e+43) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= -6.6e+17) {
		tmp = t_2;
	} else if (t <= 5.1e+36) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -3.4e+216:
		tmp = t_2
	elif t <= -2.35e+163:
		tmp = t_1
	elif t <= -2e+43:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= -6.6e+17:
		tmp = t_2
	elif t <= 5.1e+36:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -3.4e+216)
		tmp = t_2;
	elseif (t <= -2.35e+163)
		tmp = t_1;
	elseif (t <= -2e+43)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= -6.6e+17)
		tmp = t_2;
	elseif (t <= 5.1e+36)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (t * a));
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -3.4e+216)
		tmp = t_2;
	elseif (t <= -2.35e+163)
		tmp = t_1;
	elseif (t <= -2e+43)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= -6.6e+17)
		tmp = t_2;
	elseif (t <= 5.1e+36)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+216], t$95$2, If[LessEqual[t, -2.35e+163], t$95$1, If[LessEqual[t, -2e+43], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e+17], t$95$2, If[LessEqual[t, 5.1e+36], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.40000000000000026e216 or -2.00000000000000003e43 < t < -6.6e17

   1. Initial program 87.8%

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

   3. Simplified 93.8%

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

      1. pow1 93.8%

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

      2. associate-*l* 93.9%

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

      3. associate-*r* 93.8%

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

   6. Applied egg-rr 93.8%

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

      1. unpow1 93.8%

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

      2. *-commutative 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in z around inf 67.1%

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

   if -3.40000000000000026e216 < t < -2.35000000000000009e163 or 5.09999999999999973e36 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0 69.5%

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

   4. Taylor expanded in j around 0 59.2%

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

   if -2.35000000000000009e163 < t < -2.00000000000000003e43

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 59.7%

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

   4. Taylor expanded in a around 0 53.1%

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

   if -6.6e17 < t < 5.09999999999999973e36

   1. Initial program 82.8%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 58.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+216}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+163}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+17}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (* 4.0 (* t a)))) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -6.8e+216)
     t_2
     (if (<= t -3.4e+162)
       t_1
       (if (<= t -4.3e+42)
         (* b (+ c (* -27.0 (/ (* j k) b))))
         (if (<= t -1.15e+19)
           t_2
           (if (<= t 4.8e+36) (+ (* j (* k -27.0)) (* b c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -6.8e+216) {
		tmp = t_2;
	} else if (t <= -3.4e+162) {
		tmp = t_1;
	} else if (t <= -4.3e+42) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= 4.8e+36) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (t * a))
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-6.8d+216)) then
        tmp = t_2
    else if (t <= (-3.4d+162)) then
        tmp = t_1
    else if (t <= (-4.3d+42)) then
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    else if (t <= (-1.15d+19)) then
        tmp = t_2
    else if (t <= 4.8d+36) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -6.8e+216) {
		tmp = t_2;
	} else if (t <= -3.4e+162) {
		tmp = t_1;
	} else if (t <= -4.3e+42) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= 4.8e+36) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -6.8e+216:
		tmp = t_2
	elif t <= -3.4e+162:
		tmp = t_1
	elif t <= -4.3e+42:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	elif t <= -1.15e+19:
		tmp = t_2
	elif t <= 4.8e+36:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -6.8e+216)
		tmp = t_2;
	elseif (t <= -3.4e+162)
		tmp = t_1;
	elseif (t <= -4.3e+42)
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	elseif (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= 4.8e+36)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (t * a));
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -6.8e+216)
		tmp = t_2;
	elseif (t <= -3.4e+162)
		tmp = t_1;
	elseif (t <= -4.3e+42)
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	elseif (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= 4.8e+36)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+216], t$95$2, If[LessEqual[t, -3.4e+162], t$95$1, If[LessEqual[t, -4.3e+42], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e+19], t$95$2, If[LessEqual[t, 4.8e+36], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.80000000000000051e216 or -4.2999999999999998e42 < t < -1.15e19

   1. Initial program 87.8%

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

   3. Simplified 93.8%

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

      1. pow1 93.8%

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

      2. associate-*l* 93.9%

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

      3. associate-*r* 93.8%

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

   6. Applied egg-rr 93.8%

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

      1. unpow1 93.8%

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

      2. *-commutative 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in z around inf 67.1%

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

   if -6.80000000000000051e216 < t < -3.40000000000000003e162 or 4.79999999999999985e36 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0 69.5%

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

   4. Taylor expanded in j around 0 59.2%

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

   if -3.40000000000000003e162 < t < -4.2999999999999998e42

   1. Initial program 75.7%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around inf 53.1%

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

   6. Taylor expanded in b around inf 59.8%

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

   if -1.15e19 < t < 4.79999999999999985e36

   1. Initial program 82.8%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 58.7%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+216}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -28:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+24} \lor \neg \left(x \leq 1.3 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -28.0)
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (if (<= x 1.3e-25)
     (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))
     (if (or (<= x 5.8e+24) (not (<= x 1.3e+111)))
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
       (* b (+ c (* -27.0 (/ (* j k) b))))))))

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 <= -28.0) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 1.3e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if ((x <= 5.8e+24) || !(x <= 1.3e+111)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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 <= (-28.0d0)) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else if (x <= 1.3d-25) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else if ((x <= 5.8d+24) .or. (.not. (x <= 1.3d+111))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    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 <= -28.0) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 1.3e-25) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if ((x <= 5.8e+24) || !(x <= 1.3e+111)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	}
	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 <= -28.0:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	elif x <= 1.3e-25:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	elif (x <= 5.8e+24) or not (x <= 1.3e+111):
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	else:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	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 <= -28.0)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	elseif (x <= 1.3e-25)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif ((x <= 5.8e+24) || !(x <= 1.3e+111))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	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 <= -28.0)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	elseif (x <= 1.3e-25)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	elseif ((x <= 5.8e+24) || ~((x <= 1.3e+111)))
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	else
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -28.0], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-25], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.8e+24], N[Not[LessEqual[x, 1.3e+111]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -28

   1. Initial program 71.4%

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

   3. Simplified 80.4%

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

      1. pow1 80.4%

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

      2. associate-*l* 80.4%

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

      3. associate-*r* 80.4%

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

   6. Applied egg-rr 80.4%

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

      1. unpow1 80.4%

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

      2. *-commutative 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in i around 0 74.7%

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

   10. Taylor expanded in j around 0 70.4%

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

   if -28 < x < 1.3e-25

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 80.8%

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

   if 1.3e-25 < x < 5.79999999999999958e24 or 1.2999999999999999e111 < x

   1. Initial program 72.1%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in x around inf 78.1%

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

   if 5.79999999999999958e24 < x < 1.2999999999999999e111

   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 93.3%

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

   5. Taylor expanded in b around inf 67.9%

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

   6. Taylor expanded in b around inf 74.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+24} \lor \neg \left(x \leq 1.3 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.4 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (* k (* j -27.0))))
   (if (<= (* b c) -2e+108)
     (* b c)
     (if (<= (* b c) -6.4e-255)
       t_1
       (if (<= (* b c) 0.0)
         (* t (* a -4.0))
         (if (<= (* b c) 3e+232) 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 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -2e+108) {
		tmp = b * c;
	} else if ((b * c) <= -6.4e-255) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 3e+232) {
		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 = k * (j * (-27.0d0))
    if ((b * c) <= (-2d+108)) then
        tmp = b * c
    else if ((b * c) <= (-6.4d-255)) then
        tmp = t_1
    else if ((b * c) <= 0.0d0) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 3d+232) 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 = k * (j * -27.0);
	double tmp;
	if ((b * c) <= -2e+108) {
		tmp = b * c;
	} else if ((b * c) <= -6.4e-255) {
		tmp = t_1;
	} else if ((b * c) <= 0.0) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 3e+232) {
		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 = k * (j * -27.0)
	tmp = 0
	if (b * c) <= -2e+108:
		tmp = b * c
	elif (b * c) <= -6.4e-255:
		tmp = t_1
	elif (b * c) <= 0.0:
		tmp = t * (a * -4.0)
	elif (b * c) <= 3e+232:
		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(k * Float64(j * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+108)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6.4e-255)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.0)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 3e+232)
		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 = k * (j * -27.0);
	tmp = 0.0;
	if ((b * c) <= -2e+108)
		tmp = b * c;
	elseif ((b * c) <= -6.4e-255)
		tmp = t_1;
	elseif ((b * c) <= 0.0)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 3e+232)
		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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+108], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.4e-255], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.0], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e+232], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.0000000000000001e108 or 3.00000000000000003e232 < (*.f64 b c)

   1. Initial program 79.3%

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

   3. Simplified 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. Step-by-step derivation

      1. pow1 79.3%

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

      2. associate-*l* 79.3%

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

      3. associate-*r* 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow1 79.3%

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

      2. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in b around inf 58.8%

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

   if -2.0000000000000001e108 < (*.f64 b c) < -6.39999999999999985e-255 or -0.0 < (*.f64 b c) < 3.00000000000000003e232

   1. Initial program 83.5%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around inf 34.9%

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

      1. associate-*r* 34.9%

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

      2. *-commutative 34.9%

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

      3. metadata-eval 34.9%

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

      4. distribute-rgt-neg-in 34.9%

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

      5. *-commutative 34.9%

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

      6. distribute-rgt-neg-in 34.9%

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

      7. metadata-eval 34.9%

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

      8. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   if -6.39999999999999985e-255 < (*.f64 b c) < -0.0

   1. Initial program 88.6%

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

   3. Simplified 96.8%

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

      1. pow1 96.8%

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

      2. associate-*l* 96.9%

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

      3. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

      1. unpow1 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in a around inf 36.8%

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

       1. metadata-eval 36.8%

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

       2. distribute-lft-neg-in 36.8%

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

       3. associate-*r* 36.8%

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

       4. *-commutative 36.8%

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

       5. distribute-rgt-neg-in 36.8%

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

       6. distribute-lft-neg-in 36.8%

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

       7. metadata-eval 36.8%

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

       8. *-commutative 36.8%

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

   11. Simplified 36.8%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.4 \cdot 10^{-255}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 0:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+232}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* b c))) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -1.15e+165)
     t_2
     (if (<= t -2.55e+42)
       t_1
       (if (<= t -1.15e+19) t_2 (if (<= t 2.7e+241) t_1 (* t (* a -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -1.15e+165) {
		tmp = t_2;
	} else if (t <= -2.55e+42) {
		tmp = t_1;
	} else if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= 2.7e+241) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-1.15d+165)) then
        tmp = t_2
    else if (t <= (-2.55d+42)) then
        tmp = t_1
    else if (t <= (-1.15d+19)) then
        tmp = t_2
    else if (t <= 2.7d+241) then
        tmp = t_1
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -1.15e+165) {
		tmp = t_2;
	} else if (t <= -2.55e+42) {
		tmp = t_1;
	} else if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= 2.7e+241) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -1.15e+165:
		tmp = t_2
	elif t <= -2.55e+42:
		tmp = t_1
	elif t <= -1.15e+19:
		tmp = t_2
	elif t <= 2.7e+241:
		tmp = t_1
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -1.15e+165)
		tmp = t_2;
	elseif (t <= -2.55e+42)
		tmp = t_1;
	elseif (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= 2.7e+241)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -1.15e+165)
		tmp = t_2;
	elseif (t <= -2.55e+42)
		tmp = t_1;
	elseif (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= 2.7e+241)
		tmp = t_1;
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+165], t$95$2, If[LessEqual[t, -2.55e+42], t$95$1, If[LessEqual[t, -1.15e+19], t$95$2, If[LessEqual[t, 2.7e+241], t$95$1, N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000008e165 or -2.55e42 < t < -1.15e19

   1. Initial program 84.7%

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

   3. Simplified 89.1%

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

      1. pow1 89.1%

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

      2. associate-*l* 89.1%

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

      3. associate-*r* 89.1%

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

   6. Applied egg-rr 89.1%

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

      1. unpow1 89.1%

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

      2. *-commutative 89.1%

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

   8. Simplified 89.1%

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

   9. Taylor expanded in z around inf 59.3%

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

   if -1.15000000000000008e165 < t < -2.55e42 or -1.15e19 < t < 2.69999999999999972e241

   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 86.4%

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

   5. Taylor expanded in b around inf 55.2%

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

   if 2.69999999999999972e241 < t

   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 92.9%

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

      1. pow1 92.9%

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

      2. associate-*l* 92.9%

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

      3. associate-*r* 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. unpow1 92.9%

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

      2. *-commutative 92.9%

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

   8. Simplified 92.9%

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

   9. Taylor expanded in a around inf 51.3%

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

       1. metadata-eval 51.3%

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

       2. distribute-lft-neg-in 51.3%

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

       3. associate-*r* 51.3%

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

       4. *-commutative 51.3%

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

       5. distribute-rgt-neg-in 51.3%

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

       6. distribute-lft-neg-in 51.3%

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

       7. metadata-eval 51.3%

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

       8. *-commutative 51.3%

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

   11. Simplified 51.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+165}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+241}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+290}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{+90} \lor \neg \left(b \leq 6.8 \cdot 10^{-17}\right):\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= b -3.05e+290)
   (- (* b c) (* 4.0 (* t a)))
   (if (or (<= b -1.76e+90) (not (<= b 6.8e-17)))
     (* b (+ c (* -27.0 (/ (* j k) b))))
     (+ (* j (* k -27.0)) (* i (* x -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -3.05e+290) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if ((b <= -1.76e+90) || !(b <= 6.8e-17)) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (b <= (-3.05d+290)) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if ((b <= (-1.76d+90)) .or. (.not. (b <= 6.8d-17))) then
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    else
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -3.05e+290) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if ((b <= -1.76e+90) || !(b <= 6.8e-17)) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if b <= -3.05e+290:
		tmp = (b * c) - (4.0 * (t * a))
	elif (b <= -1.76e+90) or not (b <= 6.8e-17):
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	else:
		tmp = (j * (k * -27.0)) + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= -3.05e+290)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif ((b <= -1.76e+90) || !(b <= 6.8e-17))
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (b <= -3.05e+290)
		tmp = (b * c) - (4.0 * (t * a));
	elseif ((b <= -1.76e+90) || ~((b <= 6.8e-17)))
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	else
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[b, -3.05e+290], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.76e+90], N[Not[LessEqual[b, 6.8e-17]], $MachinePrecision]], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0499999999999999e290

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 63.1%

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

   4. Taylor expanded in j around 0 63.1%

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

   if -3.0499999999999999e290 < b < -1.76e90 or 6.7999999999999996e-17 < b

   1. Initial program 82.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 60.0%

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

   6. Taylor expanded in b around inf 63.8%

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

   if -1.76e90 < b < 6.7999999999999996e-17

   1. Initial program 82.8%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in i around inf 52.6%

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

      1. metadata-eval 52.6%

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

      2. distribute-lft-neg-in 52.6%

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

      3. *-commutative 52.6%

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

      4. associate-*r* 52.6%

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

      5. distribute-rgt-neg-in 52.6%

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

      6. distribute-rgt-neg-in 52.6%

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

      7. metadata-eval 52.6%

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

      8. *-commutative 52.6%

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

   7. Simplified 52.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+290}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{+90} \lor \neg \left(b \leq 6.8 \cdot 10^{-17}\right):\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+116} \lor \neg \left(b \cdot c \leq 3 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -7e+116) (not (<= (* b c) 3e+232)))
   (* 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) <= -7e+116) || !((b * c) <= 3e+232)) {
		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) <= (-7d+116)) .or. (.not. ((b * c) <= 3d+232))) 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) <= -7e+116) || !((b * c) <= 3e+232)) {
		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) <= -7e+116) or not ((b * c) <= 3e+232):
		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) <= -7e+116) || !(Float64(b * c) <= 3e+232))
		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) <= -7e+116) || ~(((b * c) <= 3e+232)))
		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], -7e+116], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3e+232]], $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) < -6.99999999999999993e116 or 3.00000000000000003e232 < (*.f64 b c)

   1. Initial program 79.3%

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

   3. Simplified 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. Step-by-step derivation

      1. pow1 79.3%

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

      2. associate-*l* 79.3%

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

      3. associate-*r* 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow1 79.3%

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

      2. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in b around inf 58.8%

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

   if -6.99999999999999993e116 < (*.f64 b c) < 3.00000000000000003e232

   1. Initial program 84.4%

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

   3. Simplified 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 32.6%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+116} \lor \neg \left(b \cdot c \leq 3 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 36.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.4 \cdot 10^{+116} \lor \neg \left(b \cdot c \leq 4.8 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= (* b c) -5.4e+116) (not (<= (* b c) 4.8e+232)))
   (* b c)
   (* 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 (((b * c) <= -5.4e+116) || !((b * c) <= 4.8e+232)) {
		tmp = b * c;
	} else {
		tmp = 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 (((b * c) <= (-5.4d+116)) .or. (.not. ((b * c) <= 4.8d+232))) then
        tmp = b * c
    else
        tmp = 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 (((b * c) <= -5.4e+116) || !((b * c) <= 4.8e+232)) {
		tmp = b * c;
	} else {
		tmp = 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 ((b * c) <= -5.4e+116) or not ((b * c) <= 4.8e+232):
		tmp = b * c
	else:
		tmp = 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 ((Float64(b * c) <= -5.4e+116) || !(Float64(b * c) <= 4.8e+232))
		tmp = Float64(b * c);
	else
		tmp = 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 (((b * c) <= -5.4e+116) || ~(((b * c) <= 4.8e+232)))
		tmp = b * c;
	else
		tmp = 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[N[(b * c), $MachinePrecision], -5.4e+116], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4.8e+232]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.3999999999999999e116 or 4.8000000000000003e232 < (*.f64 b c)

   1. Initial program 79.3%

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

   3. Simplified 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. Step-by-step derivation

      1. pow1 79.3%

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

      2. associate-*l* 79.3%

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

      3. associate-*r* 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow1 79.3%

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

      2. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in b around inf 58.8%

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

   if -5.3999999999999999e116 < (*.f64 b c) < 4.8000000000000003e232

   1. Initial program 84.4%

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

   3. Simplified 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 32.6%

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

      1. associate-*r* 32.6%

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

      2. *-commutative 32.6%

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

      3. metadata-eval 32.6%

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

      4. distribute-rgt-neg-in 32.6%

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

      5. *-commutative 32.6%

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

      6. distribute-rgt-neg-in 32.6%

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

      7. metadata-eval 32.6%

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

      8. *-commutative 32.6%

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

   7. Simplified 32.6%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.4 \cdot 10^{+116} \lor \neg \left(b \cdot c \leq 4.8 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 23.3% 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 83.0%

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

3. Simplified 85.7%

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

   1. pow1 85.7%

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

   2. associate-*l* 85.7%

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

   3. associate-*r* 85.7%

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

6. Applied egg-rr 85.7%

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

   1. unpow1 85.7%

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

   2. *-commutative 85.7%

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

8. Simplified 85.7%

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

9. Taylor expanded in b around inf 22.9%

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

10. Final simplification 22.9%

    \[\leadsto b \cdot c \]
11. Add Preprocessing

Developer target: 89.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024060 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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