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

Percentage Accurate: 85.0% → 88.1%

Time: 25.5s

Alternatives: 22

Speedup: 0.8×

• 50.4% 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: 85.0% 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: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-69} \lor \neg \left(t \leq 2.55 \cdot 10^{-172}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -6.6e-69) (not (<= t 2.55e-172)))
   (-
    (+ (* b c) (* t (- (* x (* z (* 18.0 y))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.6e-69) || !(t <= 2.55e-172)) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-6.6d-69)) .or. (.not. (t <= 2.55d-172))) then
        tmp = ((b * c) + (t * ((x * (z * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.6e-69) || !(t <= 2.55e-172)) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -6.6e-69) or not (t <= 2.55e-172):
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -6.6e-69) || !(t <= 2.55e-172))
		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(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -6.6e-69) || ~((t <= 2.55e-172)))
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -6.6e-69], N[Not[LessEqual[t, 2.55e-172]], $MachinePrecision]], 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[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000001e-69 or 2.5499999999999999e-172 < t

   1. Initial program 87.5%

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

   3. Simplified 91.8%

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

      1. pow1 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-*r* 91.7%

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

   6. Applied egg-rr 91.7%

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

      1. unpow1 91.7%

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

      2. *-commutative 91.7%

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

   8. Simplified 91.7%

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

   if -6.6000000000000001e-69 < t < 2.5499999999999999e-172

   1. Initial program 76.8%

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

   3. Taylor expanded in y around 0 93.1%

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

      1. distribute-lft-out 93.1%

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

      2. *-commutative 93.1%

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

   5. Simplified 93.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-69} \lor \neg \left(t \leq 2.55 \cdot 10^{-172}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.2%

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

   3. Simplified 96.1%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in t around 0 41.4%

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

   6. Taylor expanded in x around inf 55.2%

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

4. Final simplification 91.4%

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

Alternative 3: 44.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := -18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-97}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{c}{i} + x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-193}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* a (* t -4.0))) (t_2 (* -18.0 (* t (* x (* y (- z)))))))
   (if (<= t -3.9e+156)
     t_2
     (if (<= t -8.5e+68)
       t_1
       (if (<= t -3.3e+19)
         t_2
         (if (<= t -2.85e-56)
           (* b (+ c (* -4.0 (* i (/ x b)))))
           (if (<= t -6.5e-97)
             (* i (+ (* b (/ c i)) (* x -4.0)))
             (if (<= t 3.6e-193)
               (- (* b c) (* 27.0 (* j k)))
               (if (<= t 1.1e+123)
                 (- (* b c) (* x (* 4.0 i)))
                 (if (<= t 1.3e+224) t_1 t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = -18.0 * (t * (x * (y * -z)));
	double tmp;
	if (t <= -3.9e+156) {
		tmp = t_2;
	} else if (t <= -8.5e+68) {
		tmp = t_1;
	} else if (t <= -3.3e+19) {
		tmp = t_2;
	} else if (t <= -2.85e-56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if (t <= -6.5e-97) {
		tmp = i * ((b * (c / i)) + (x * -4.0));
	} else if (t <= 3.6e-193) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1.1e+123) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.3e+224) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * (-4.0d0))
    t_2 = (-18.0d0) * (t * (x * (y * -z)))
    if (t <= (-3.9d+156)) then
        tmp = t_2
    else if (t <= (-8.5d+68)) then
        tmp = t_1
    else if (t <= (-3.3d+19)) then
        tmp = t_2
    else if (t <= (-2.85d-56)) then
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    else if (t <= (-6.5d-97)) then
        tmp = i * ((b * (c / i)) + (x * (-4.0d0)))
    else if (t <= 3.6d-193) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 1.1d+123) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 1.3d+224) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = -18.0 * (t * (x * (y * -z)));
	double tmp;
	if (t <= -3.9e+156) {
		tmp = t_2;
	} else if (t <= -8.5e+68) {
		tmp = t_1;
	} else if (t <= -3.3e+19) {
		tmp = t_2;
	} else if (t <= -2.85e-56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if (t <= -6.5e-97) {
		tmp = i * ((b * (c / i)) + (x * -4.0));
	} else if (t <= 3.6e-193) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1.1e+123) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.3e+224) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (t * -4.0)
	t_2 = -18.0 * (t * (x * (y * -z)))
	tmp = 0
	if t <= -3.9e+156:
		tmp = t_2
	elif t <= -8.5e+68:
		tmp = t_1
	elif t <= -3.3e+19:
		tmp = t_2
	elif t <= -2.85e-56:
		tmp = b * (c + (-4.0 * (i * (x / b))))
	elif t <= -6.5e-97:
		tmp = i * ((b * (c / i)) + (x * -4.0))
	elif t <= 3.6e-193:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 1.1e+123:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 1.3e+224:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(t * -4.0))
	t_2 = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))))
	tmp = 0.0
	if (t <= -3.9e+156)
		tmp = t_2;
	elseif (t <= -8.5e+68)
		tmp = t_1;
	elseif (t <= -3.3e+19)
		tmp = t_2;
	elseif (t <= -2.85e-56)
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	elseif (t <= -6.5e-97)
		tmp = Float64(i * Float64(Float64(b * Float64(c / i)) + Float64(x * -4.0)));
	elseif (t <= 3.6e-193)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.1e+123)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 1.3e+224)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (t * -4.0);
	t_2 = -18.0 * (t * (x * (y * -z)));
	tmp = 0.0;
	if (t <= -3.9e+156)
		tmp = t_2;
	elseif (t <= -8.5e+68)
		tmp = t_1;
	elseif (t <= -3.3e+19)
		tmp = t_2;
	elseif (t <= -2.85e-56)
		tmp = b * (c + (-4.0 * (i * (x / b))));
	elseif (t <= -6.5e-97)
		tmp = i * ((b * (c / i)) + (x * -4.0));
	elseif (t <= 3.6e-193)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 1.1e+123)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 1.3e+224)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+156], t$95$2, If[LessEqual[t, -8.5e+68], t$95$1, If[LessEqual[t, -3.3e+19], t$95$2, If[LessEqual[t, -2.85e-56], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-97], N[(i * N[(N[(b * N[(c / i), $MachinePrecision]), $MachinePrecision] + N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-193], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+123], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+224], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.8999999999999997e156 or -8.49999999999999966e68 < t < -3.3e19 or 1.3e224 < t

   1. Initial program 88.4%

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

   3. Simplified 92.2%

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

      1. pow1 92.2%

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

      2. associate-*l* 92.2%

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

      3. associate-*r* 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. unpow1 92.2%

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

      2. *-commutative 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in x around -inf 62.3%

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

       1. mul-1-neg 62.3%

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

       2. cancel-sign-sub-inv 62.3%

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

       3. associate-*r* 62.4%

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

       4. metadata-eval 62.4%

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

   11. Simplified 62.4%

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

   12. Taylor expanded in t around inf 58.7%

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

   if -3.8999999999999997e156 < t < -8.49999999999999966e68 or 1.09999999999999996e123 < t < 1.3e224

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. distribute-lft-out 80.6%

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

      2. *-commutative 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in t around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*l* 58.8%

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

   8. Simplified 58.8%

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

   if -3.3e19 < t < -2.8499999999999999e-56

   1. Initial program 92.2%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 52.1%

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

   6. Taylor expanded in i around inf 43.9%

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

      1. associate-*r* 43.9%

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

      2. *-commutative 43.9%

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

   8. Simplified 43.9%

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

   9. Taylor expanded in b around inf 43.9%

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

       1. associate-/l* 52.0%

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

   11. Simplified 52.0%

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

   if -2.8499999999999999e-56 < t < -6.5000000000000004e-97

   1. Initial program 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 89.6%

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

   6. Taylor expanded in i around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in i around inf 78.0%

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

       1. cancel-sign-sub-inv 78.0%

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

       2. metadata-eval 78.0%

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

       3. associate-/l* 78.0%

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

       4. *-commutative 78.0%

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

   11. Simplified 78.0%

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

   if -6.5000000000000004e-97 < t < 3.5999999999999999e-193

   1. Initial program 75.5%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in x around 0 77.0%

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

   6. Taylor expanded in a around 0 73.7%

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

   if 3.5999999999999999e-193 < t < 1.09999999999999996e123

   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 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. Taylor expanded in t around 0 67.1%

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

   6. Taylor expanded in i around inf 56.1%

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

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

      \[\leadsto b \cdot c - \color{blue}{x \cdot \left(4 \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+156}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-97}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{c}{i} + x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-193}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+224}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-191}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (+ (* x i) (* t a)))))
        (t_2 (* t (- (* a (- 4.0)) (* (* x (* y z)) -18.0)))))
   (if (<= t -1.05e-73)
     t_2
     (if (<= t 2.15e-191)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= t 6.7e-79)
         t_1
         (if (<= t 8e+36)
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
           (if (<= t 1.3e+99) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double t_2 = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	double tmp;
	if (t <= -1.05e-73) {
		tmp = t_2;
	} else if (t <= 2.15e-191) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 6.7e-79) {
		tmp = t_1;
	} else if (t <= 8e+36) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 1.3e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    t_2 = t * ((a * -4.0d0) - ((x * (y * z)) * (-18.0d0)))
    if (t <= (-1.05d-73)) then
        tmp = t_2
    else if (t <= 2.15d-191) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 6.7d-79) then
        tmp = t_1
    else if (t <= 8d+36) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= 1.3d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double t_2 = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	double tmp;
	if (t <= -1.05e-73) {
		tmp = t_2;
	} else if (t <= 2.15e-191) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 6.7e-79) {
		tmp = t_1;
	} else if (t <= 8e+36) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 1.3e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * ((x * i) + (t * a)))
	t_2 = t * ((a * -4.0) - ((x * (y * z)) * -18.0))
	tmp = 0
	if t <= -1.05e-73:
		tmp = t_2
	elif t <= 2.15e-191:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 6.7e-79:
		tmp = t_1
	elif t <= 8e+36:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= 1.3e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	t_2 = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(x * Float64(y * z)) * -18.0)))
	tmp = 0.0
	if (t <= -1.05e-73)
		tmp = t_2;
	elseif (t <= 2.15e-191)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 6.7e-79)
		tmp = t_1;
	elseif (t <= 8e+36)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= 1.3e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * ((x * i) + (t * a)));
	t_2 = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	tmp = 0.0;
	if (t <= -1.05e-73)
		tmp = t_2;
	elseif (t <= 2.15e-191)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 6.7e-79)
		tmp = t_1;
	elseif (t <= 8e+36)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= 1.3e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-73], t$95$2, If[LessEqual[t, 2.15e-191], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.7e-79], t$95$1, If[LessEqual[t, 8e+36], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+99], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0499999999999999e-73 or 1.3e99 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. associate-*r* 78.3%

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

      2. neg-mul-1 78.3%

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

      3. cancel-sign-sub-inv 78.3%

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

      4. metadata-eval 78.3%

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

      5. *-commutative 78.3%

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

      6. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -1.0499999999999999e-73 < t < 2.14999999999999992e-191

   1. Initial program 76.2%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in x around 0 74.6%

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

   6. Taylor expanded in a around 0 71.7%

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

   if 2.14999999999999992e-191 < t < 6.70000000000000017e-79 or 8.00000000000000034e36 < t < 1.3e99

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 82.9%

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

      1. distribute-lft-out 82.9%

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

      2. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in j around 0 74.0%

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

   if 6.70000000000000017e-79 < t < 8.00000000000000034e36

   1. Initial program 87.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 71.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-191}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-79}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+99}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* b (+ c (* -4.0 (* i (/ x b)))))))
   (if (<= (* b c) -1e-64)
     t_1
     (if (<= (* b c) -2e-116)
       (* a (* t -4.0))
       (if (<= (* b c) -1e-279)
         (* -18.0 (* t (* x (* y (- z)))))
         (if (<= (* b c) 5e+48)
           (+ (* j (* k -27.0)) (* i (* x -4.0)))
           t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = b * (c + (-4.0 * (i * (x / b))));
	double tmp;
	if ((b * c) <= -1e-64) {
		tmp = t_1;
	} else if ((b * c) <= -2e-116) {
		tmp = a * (t * -4.0);
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 5e+48) {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (c + ((-4.0d0) * (i * (x / b))))
    if ((b * c) <= (-1d-64)) then
        tmp = t_1
    else if ((b * c) <= (-2d-116)) then
        tmp = a * (t * (-4.0d0))
    else if ((b * c) <= (-1d-279)) then
        tmp = (-18.0d0) * (t * (x * (y * -z)))
    else if ((b * c) <= 5d+48) then
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * (i * (x / b))));
	double tmp;
	if ((b * c) <= -1e-64) {
		tmp = t_1;
	} else if ((b * c) <= -2e-116) {
		tmp = a * (t * -4.0);
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 5e+48) {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = b * (c + (-4.0 * (i * (x / b))))
	tmp = 0
	if (b * c) <= -1e-64:
		tmp = t_1
	elif (b * c) <= -2e-116:
		tmp = a * (t * -4.0)
	elif (b * c) <= -1e-279:
		tmp = -18.0 * (t * (x * (y * -z)))
	elif (b * c) <= 5e+48:
		tmp = (j * (k * -27.0)) + (i * (x * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))))
	tmp = 0.0
	if (Float64(b * c) <= -1e-64)
		tmp = t_1;
	elseif (Float64(b * c) <= -2e-116)
		tmp = Float64(a * Float64(t * -4.0));
	elseif (Float64(b * c) <= -1e-279)
		tmp = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))));
	elseif (Float64(b * c) <= 5e+48)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = b * (c + (-4.0 * (i * (x / b))));
	tmp = 0.0;
	if ((b * c) <= -1e-64)
		tmp = t_1;
	elseif ((b * c) <= -2e-116)
		tmp = a * (t * -4.0);
	elseif ((b * c) <= -1e-279)
		tmp = -18.0 * (t * (x * (y * -z)));
	elseif ((b * c) <= 5e+48)
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e-64], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2e-116], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-279], N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+48], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -9.99999999999999965e-65 or 4.99999999999999973e48 < (*.f64 b c)

   1. Initial program 80.4%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in t around 0 65.7%

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

   6. Taylor expanded in i around inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in b around inf 57.3%

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

       1. associate-/l* 57.9%

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

   11. Simplified 57.9%

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

   if -9.99999999999999965e-65 < (*.f64 b c) < -2e-116

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. distribute-lft-out 91.4%

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

      2. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in t around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-*l* 73.3%

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

   8. Simplified 73.3%

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

   if -2e-116 < (*.f64 b c) < -1.00000000000000006e-279

   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 89.9%

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

      1. pow1 89.9%

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

      2. associate-*l* 89.8%

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

      3. associate-*r* 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. unpow1 89.8%

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

      2. *-commutative 89.8%

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

   8. Simplified 89.8%

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

   9. Taylor expanded in x around -inf 80.4%

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

       1. mul-1-neg 80.4%

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

       2. cancel-sign-sub-inv 80.4%

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

       3. associate-*r* 80.3%

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

       4. metadata-eval 80.3%

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

   11. Simplified 80.3%

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

   12. Taylor expanded in t around inf 63.5%

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

   if -1.00000000000000006e-279 < (*.f64 b c) < 4.99999999999999973e48

   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 90.9%

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

   5. Taylor expanded in i around inf 53.4%

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

      1. metadata-eval 53.4%

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

      2. distribute-lft-neg-in 53.4%

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

      3. *-commutative 53.4%

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

      4. associate-*r* 53.4%

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

      5. distribute-rgt-neg-in 53.4%

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

      6. distribute-rgt-neg-in 53.4%

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

      7. metadata-eval 53.4%

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

      8. *-commutative 53.4%

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

   7. Simplified 53.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-64}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* a (* t -4.0)))))
   (if (<= (* b c) -2e+56)
     (* b (+ c (* -4.0 (* i (/ x b)))))
     (if (<= (* b c) -2e-116)
       t_1
       (if (<= (* b c) -1e-279)
         (* -18.0 (* t (* x (* y (- z)))))
         (if (<= (* b c) 2e+120) t_1 (- (* b c) (* x (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	double tmp;
	if ((b * c) <= -2e+56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if ((b * c) <= -2e-116) {
		tmp = t_1;
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 2e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    if ((b * c) <= (-2d+56)) then
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    else if ((b * c) <= (-2d-116)) then
        tmp = t_1
    else if ((b * c) <= (-1d-279)) then
        tmp = (-18.0d0) * (t * (x * (y * -z)))
    else if ((b * c) <= 2d+120) then
        tmp = t_1
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	double tmp;
	if ((b * c) <= -2e+56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if ((b * c) <= -2e-116) {
		tmp = t_1;
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 2e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (a * (t * -4.0))
	tmp = 0
	if (b * c) <= -2e+56:
		tmp = b * (c + (-4.0 * (i * (x / b))))
	elif (b * c) <= -2e-116:
		tmp = t_1
	elif (b * c) <= -1e-279:
		tmp = -18.0 * (t * (x * (y * -z)))
	elif (b * c) <= 2e+120:
		tmp = t_1
	else:
		tmp = (b * c) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -2e+56)
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	elseif (Float64(b * c) <= -2e-116)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-279)
		tmp = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))));
	elseif (Float64(b * c) <= 2e+120)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	tmp = 0.0;
	if ((b * c) <= -2e+56)
		tmp = b * (c + (-4.0 * (i * (x / b))));
	elseif ((b * c) <= -2e-116)
		tmp = t_1;
	elseif ((b * c) <= -1e-279)
		tmp = -18.0 * (t * (x * (y * -z)));
	elseif ((b * c) <= 2e+120)
		tmp = t_1;
	else
		tmp = (b * c) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+56], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-116], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-279], N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+120], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.00000000000000018e56

   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 87.2%

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

   5. Taylor expanded in t around 0 68.9%

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

   6. Taylor expanded in i around inf 62.5%

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

      1. associate-*r* 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in b around inf 60.5%

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

       1. associate-/l* 60.5%

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

   11. Simplified 60.5%

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

   if -2.00000000000000018e56 < (*.f64 b c) < -2e-116 or -1.00000000000000006e-279 < (*.f64 b c) < 2e120

   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 89.9%

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

   5. Taylor expanded in a around inf 56.4%

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

      1. metadata-eval 56.4%

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

      2. distribute-lft-neg-in 56.4%

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

      3. *-commutative 56.4%

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

      4. associate-*l* 56.4%

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

      5. distribute-lft-neg-in 56.4%

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

      6. distribute-lft-neg-in 56.4%

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

      7. metadata-eval 56.4%

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

   7. Simplified 56.4%

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

   if -2e-116 < (*.f64 b c) < -1.00000000000000006e-279

   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 89.9%

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

      1. pow1 89.9%

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

      2. associate-*l* 89.8%

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

      3. associate-*r* 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. unpow1 89.8%

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

      2. *-commutative 89.8%

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

   8. Simplified 89.8%

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

   9. Taylor expanded in x around -inf 80.4%

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

       1. mul-1-neg 80.4%

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

       2. cancel-sign-sub-inv 80.4%

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

       3. associate-*r* 80.3%

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

       4. metadata-eval 80.3%

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

   11. Simplified 80.3%

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

   12. Taylor expanded in t around inf 63.5%

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

   if 2e120 < (*.f64 b c)

   1. Initial program 74.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 75.0%

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

   6. Taylor expanded in i around inf 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

   8. Simplified 69.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* (* t a) -4.0) (* 27.0 (* j k)))))
   (if (<= (* b c) -2e+56)
     (* b (+ c (* -4.0 (* i (/ x b)))))
     (if (<= (* b c) -2e-116)
       t_1
       (if (<= (* b c) -1e-279)
         (* -18.0 (* t (* x (* y (- z)))))
         (if (<= (* b c) 2e+120) t_1 (- (* b c) (* x (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	double tmp;
	if ((b * c) <= -2e+56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if ((b * c) <= -2e-116) {
		tmp = t_1;
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 2e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) * (-4.0d0)) - (27.0d0 * (j * k))
    if ((b * c) <= (-2d+56)) then
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    else if ((b * c) <= (-2d-116)) then
        tmp = t_1
    else if ((b * c) <= (-1d-279)) then
        tmp = (-18.0d0) * (t * (x * (y * -z)))
    else if ((b * c) <= 2d+120) then
        tmp = t_1
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	double tmp;
	if ((b * c) <= -2e+56) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if ((b * c) <= -2e-116) {
		tmp = t_1;
	} else if ((b * c) <= -1e-279) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if ((b * c) <= 2e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((t * a) * -4.0) - (27.0 * (j * k))
	tmp = 0
	if (b * c) <= -2e+56:
		tmp = b * (c + (-4.0 * (i * (x / b))))
	elif (b * c) <= -2e-116:
		tmp = t_1
	elif (b * c) <= -1e-279:
		tmp = -18.0 * (t * (x * (y * -z)))
	elif (b * c) <= 2e+120:
		tmp = t_1
	else:
		tmp = (b * c) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(t * a) * -4.0) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (Float64(b * c) <= -2e+56)
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	elseif (Float64(b * c) <= -2e-116)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-279)
		tmp = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))));
	elseif (Float64(b * c) <= 2e+120)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	tmp = 0.0;
	if ((b * c) <= -2e+56)
		tmp = b * (c + (-4.0 * (i * (x / b))));
	elseif ((b * c) <= -2e-116)
		tmp = t_1;
	elseif ((b * c) <= -1e-279)
		tmp = -18.0 * (t * (x * (y * -z)));
	elseif ((b * c) <= 2e+120)
		tmp = t_1;
	else
		tmp = (b * c) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+56], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-116], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-279], N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+120], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.00000000000000018e56

   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 87.2%

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

   5. Taylor expanded in t around 0 68.9%

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

   6. Taylor expanded in i around inf 62.5%

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

      1. associate-*r* 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in b around inf 60.5%

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

       1. associate-/l* 60.5%

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

   11. Simplified 60.5%

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

   if -2.00000000000000018e56 < (*.f64 b c) < -2e-116 or -1.00000000000000006e-279 < (*.f64 b c) < 2e120

   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 89.9%

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

   5. Taylor expanded in x around 0 61.4%

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

   6. Taylor expanded in b around 0 56.5%

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

   if -2e-116 < (*.f64 b c) < -1.00000000000000006e-279

   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 89.9%

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

      1. pow1 89.9%

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

      2. associate-*l* 89.8%

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

      3. associate-*r* 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. unpow1 89.8%

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

      2. *-commutative 89.8%

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

   8. Simplified 89.8%

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

   9. Taylor expanded in x around -inf 80.4%

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

       1. mul-1-neg 80.4%

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

       2. cancel-sign-sub-inv 80.4%

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

       3. associate-*r* 80.3%

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

       4. metadata-eval 80.3%

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

   11. Simplified 80.3%

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

   12. Taylor expanded in t around inf 63.5%

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

   if 2e120 < (*.f64 b c)

   1. Initial program 74.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 75.0%

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

   6. Taylor expanded in i around inf 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

   8. Simplified 69.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-279}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := -18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* a (* t -4.0))) (t_2 (* -18.0 (* t (* x (* y (- z)))))))
   (if (<= t -1.1e+157)
     t_2
     (if (<= t -6.5e+18)
       t_1
       (if (<= t 9.2e-192)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= t 2.65e+123)
           (- (* b c) (* x (* 4.0 i)))
           (if (<= t 1e+226) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = -18.0 * (t * (x * (y * -z)));
	double tmp;
	if (t <= -1.1e+157) {
		tmp = t_2;
	} else if (t <= -6.5e+18) {
		tmp = t_1;
	} else if (t <= 9.2e-192) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 2.65e+123) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * (-4.0d0))
    t_2 = (-18.0d0) * (t * (x * (y * -z)))
    if (t <= (-1.1d+157)) then
        tmp = t_2
    else if (t <= (-6.5d+18)) then
        tmp = t_1
    else if (t <= 9.2d-192) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 2.65d+123) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 1d+226) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = -18.0 * (t * (x * (y * -z)));
	double tmp;
	if (t <= -1.1e+157) {
		tmp = t_2;
	} else if (t <= -6.5e+18) {
		tmp = t_1;
	} else if (t <= 9.2e-192) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 2.65e+123) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (t * -4.0)
	t_2 = -18.0 * (t * (x * (y * -z)))
	tmp = 0
	if t <= -1.1e+157:
		tmp = t_2
	elif t <= -6.5e+18:
		tmp = t_1
	elif t <= 9.2e-192:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 2.65e+123:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 1e+226:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(t * -4.0))
	t_2 = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))))
	tmp = 0.0
	if (t <= -1.1e+157)
		tmp = t_2;
	elseif (t <= -6.5e+18)
		tmp = t_1;
	elseif (t <= 9.2e-192)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 2.65e+123)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 1e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (t * -4.0);
	t_2 = -18.0 * (t * (x * (y * -z)));
	tmp = 0.0;
	if (t <= -1.1e+157)
		tmp = t_2;
	elseif (t <= -6.5e+18)
		tmp = t_1;
	elseif (t <= 9.2e-192)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 2.65e+123)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 1e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+157], t$95$2, If[LessEqual[t, -6.5e+18], t$95$1, If[LessEqual[t, 9.2e-192], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+123], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+226], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1000000000000001e157 or 9.99999999999999961e225 < t

   1. Initial program 88.3%

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

   3. Simplified 93.0%

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

      1. pow1 93.0%

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

      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* 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow1 93.0%

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

      2. *-commutative 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in x around -inf 63.6%

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

       1. mul-1-neg 63.6%

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

       2. cancel-sign-sub-inv 63.6%

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

       3. associate-*r* 63.6%

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

       4. metadata-eval 63.6%

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

   11. Simplified 63.6%

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

   12. Taylor expanded in t around inf 59.1%

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

   if -1.1000000000000001e157 < t < -6.5e18 or 2.65e123 < t < 9.99999999999999961e225

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 75.1%

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

      1. distribute-lft-out 75.1%

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

      2. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*l* 52.4%

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

   8. Simplified 52.4%

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

   if -6.5e18 < t < 9.20000000000000073e-192

   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 79.2%

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

   5. Taylor expanded in x around 0 73.0%

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

   6. Taylor expanded in a around 0 67.0%

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

   if 9.20000000000000073e-192 < t < 2.65e123

   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 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. Taylor expanded in t around 0 67.1%

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

   6. Taylor expanded in i around inf 56.1%

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

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{+226}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+103}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-318}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* a (* t -4.0))))
   (if (<= (* b c) -2.7e+103)
     (* b c)
     (if (<= (* b c) -7.5e-257)
       t_1
       (if (<= (* b c) 1e-318)
         (* (* j k) -27.0)
         (if (<= (* b c) 4.3e+154) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -2.7e+103) {
		tmp = b * c;
	} else if ((b * c) <= -7.5e-257) {
		tmp = t_1;
	} else if ((b * c) <= 1e-318) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 4.3e+154) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (-4.0d0))
    if ((b * c) <= (-2.7d+103)) then
        tmp = b * c
    else if ((b * c) <= (-7.5d-257)) then
        tmp = t_1
    else if ((b * c) <= 1d-318) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 4.3d+154) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -2.7e+103) {
		tmp = b * c;
	} else if ((b * c) <= -7.5e-257) {
		tmp = t_1;
	} else if ((b * c) <= 1e-318) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 4.3e+154) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (t * -4.0)
	tmp = 0
	if (b * c) <= -2.7e+103:
		tmp = b * c
	elif (b * c) <= -7.5e-257:
		tmp = t_1
	elif (b * c) <= 1e-318:
		tmp = (j * k) * -27.0
	elif (b * c) <= 4.3e+154:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.7e+103)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.5e-257)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-318)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 4.3e+154)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (t * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.7e+103)
		tmp = b * c;
	elseif ((b * c) <= -7.5e-257)
		tmp = t_1;
	elseif ((b * c) <= 1e-318)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 4.3e+154)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.7e+103], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.5e-257], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-318], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.3e+154], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.69999999999999993e103 or 4.2999999999999998e154 < (*.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 82.4%

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

      1. pow1 82.4%

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

      2. associate-*l* 82.4%

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

      3. associate-*r* 82.4%

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

   6. Applied egg-rr 82.4%

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

      1. unpow1 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in b around inf 59.1%

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

   if -2.69999999999999993e103 < (*.f64 b c) < -7.4999999999999995e-257 or 9.9999875e-319 < (*.f64 b c) < 4.2999999999999998e154

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. distribute-lft-out 74.3%

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

      2. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around inf 33.9%

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

      1. *-commutative 33.9%

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

      2. associate-*l* 33.9%

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

   8. Simplified 33.9%

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

   if -7.4999999999999995e-257 < (*.f64 b c) < 9.9999875e-319

   1. Initial program 88.8%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 43.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+103}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-318}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-318}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* a (* t -4.0))))
   (if (<= (* b c) -2.8e+88)
     (* b c)
     (if (<= (* b c) -1.8e-264)
       t_1
       (if (<= (* b c) 1e-318)
         (* k (* j -27.0))
         (if (<= (* b c) 8.2e+157) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -2.8e+88) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-264) {
		tmp = t_1;
	} else if ((b * c) <= 1e-318) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8.2e+157) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (-4.0d0))
    if ((b * c) <= (-2.8d+88)) then
        tmp = b * c
    else if ((b * c) <= (-1.8d-264)) then
        tmp = t_1
    else if ((b * c) <= 1d-318) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 8.2d+157) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -2.8e+88) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-264) {
		tmp = t_1;
	} else if ((b * c) <= 1e-318) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8.2e+157) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (t * -4.0)
	tmp = 0
	if (b * c) <= -2.8e+88:
		tmp = b * c
	elif (b * c) <= -1.8e-264:
		tmp = t_1
	elif (b * c) <= 1e-318:
		tmp = k * (j * -27.0)
	elif (b * c) <= 8.2e+157:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.8e+88)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.8e-264)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-318)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 8.2e+157)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (t * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.8e+88)
		tmp = b * c;
	elseif ((b * c) <= -1.8e-264)
		tmp = t_1;
	elseif ((b * c) <= 1e-318)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 8.2e+157)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.8e+88], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.8e-264], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-318], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.2e+157], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.79999999999999989e88 or 8.20000000000000032e157 < (*.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 82.4%

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

      1. pow1 82.4%

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

      2. associate-*l* 82.4%

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

      3. associate-*r* 82.4%

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

   6. Applied egg-rr 82.4%

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

      1. unpow1 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in b around inf 59.1%

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

   if -2.79999999999999989e88 < (*.f64 b c) < -1.8000000000000001e-264 or 9.9999875e-319 < (*.f64 b c) < 8.20000000000000032e157

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. distribute-lft-out 74.3%

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

      2. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around inf 33.9%

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

      1. *-commutative 33.9%

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

      2. associate-*l* 33.9%

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

   8. Simplified 33.9%

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

   if -1.8000000000000001e-264 < (*.f64 b c) < 9.9999875e-319

   1. Initial program 88.8%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 43.2%

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

      1. associate-*r* 43.3%

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

      2. *-commutative 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-318}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-65} \lor \neg \left(t \leq 96000000000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.85e-65) (not (<= t 96000000000000.0)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 4.0 (* x i)))
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.85e-65) || !(t <= 96000000000000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.85d-65)) .or. (.not. (t <= 96000000000000.0d0))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.85e-65) || !(t <= 96000000000000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.85e-65) or not (t <= 96000000000000.0):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.85e-65) || !(t <= 96000000000000.0))
		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(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.85e-65) || ~((t <= 96000000000000.0)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.85e-65], N[Not[LessEqual[t, 96000000000000.0]], $MachinePrecision]], 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[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85e-65 or 9.6e13 < t

   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 92.8%

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

   5. Taylor expanded in j around 0 90.0%

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

   if -1.85e-65 < t < 9.6e13

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. distribute-lft-out 88.1%

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

      2. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-65} \lor \neg \left(t \leq 96000000000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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))))))
   (if (<= t -9.5e-68)
     (- t_1 (* 27.0 (* j k)))
     (if (<= t 1.25e+14)
       (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))
       (- t_1 (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -9.5e-68) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 1.25e+14) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = t_1 - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-9.5d-68)) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (t <= 1.25d+14) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    else
        tmp = t_1 - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -9.5e-68) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 1.25e+14) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = t_1 - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -9.5e-68:
		tmp = t_1 - (27.0 * (j * k))
	elif t <= 1.25e+14:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	else:
		tmp = t_1 - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -9.5e-68)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.25e+14)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -9.5e-68)
		tmp = t_1 - (27.0 * (j * k));
	elseif (t <= 1.25e+14)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	else
		tmp = t_1 - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-68], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+14], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999997e-68

   1. Initial program 90.4%

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

   3. Simplified 95.2%

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

      1. pow1 95.2%

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

      2. associate-*l* 95.1%

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

      3. associate-*r* 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. unpow1 95.1%

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

      2. *-commutative 95.1%

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

   8. Simplified 95.1%

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

   9. Taylor expanded in i around 0 92.5%

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

   if -9.4999999999999997e-68 < t < 1.25e14

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. distribute-lft-out 88.1%

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

      2. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   if 1.25e14 < t

   1. Initial program 85.8%

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

   3. Simplified 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 j around 0 89.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-64} \lor \neg \left(t \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.3e-64) (not (<= t 1.38e+14)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.3e-64) || !(t <= 1.38e+14)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.3d-64)) .or. (.not. (t <= 1.38d+14))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.3e-64) || !(t <= 1.38e+14)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.3e-64) or not (t <= 1.38e+14):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.3e-64) || !(t <= 1.38e+14))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.3e-64) || ~((t <= 1.38e+14)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.3e-64], N[Not[LessEqual[t, 1.38e+14]], $MachinePrecision]], 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[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e-64 or 1.38e14 < t

   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 92.8%

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

      1. pow1 92.8%

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

      2. associate-*l* 92.7%

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

      3. associate-*r* 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. unpow1 92.7%

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

      2. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in i around 0 87.7%

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

   10. Taylor expanded in j around 0 84.9%

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

   if -1.3e-64 < t < 1.38e14

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. distribute-lft-out 88.1%

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

      2. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-64} \lor \neg \left(t \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 17000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -1.75e+160)
     t_1
     (if (<= x 5.2e-182)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 17000000000.0) (+ (* j (* k -27.0)) (* a (* t -4.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.75e+160) {
		tmp = t_1;
	} else if (x <= 5.2e-182) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 17000000000.0) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-1.75d+160)) then
        tmp = t_1
    else if (x <= 5.2d-182) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 17000000000.0d0) then
        tmp = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.75e+160) {
		tmp = t_1;
	} else if (x <= 5.2e-182) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 17000000000.0) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -1.75e+160:
		tmp = t_1
	elif x <= 5.2e-182:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 17000000000.0:
		tmp = (j * (k * -27.0)) + (a * (t * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -1.75e+160)
		tmp = t_1;
	elseif (x <= 5.2e-182)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 17000000000.0)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -1.75e+160)
		tmp = t_1;
	elseif (x <= 5.2e-182)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 17000000000.0)
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+160], t$95$1, If[LessEqual[x, 5.2e-182], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 17000000000.0], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75000000000000013e160 or 1.7e10 < x

   1. Initial program 73.6%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in x around inf 69.3%

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

   if -1.75000000000000013e160 < x < 5.20000000000000011e-182

   1. Initial program 89.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around 0 79.0%

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

   6. Taylor expanded in a around 0 62.8%

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

   if 5.20000000000000011e-182 < x < 1.7e10

   1. Initial program 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around inf 61.1%

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

      1. metadata-eval 61.1%

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

      2. distribute-lft-neg-in 61.1%

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

      3. *-commutative 61.1%

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

      4. associate-*l* 61.1%

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

      5. distribute-lft-neg-in 61.1%

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

      6. distribute-lft-neg-in 61.1%

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

      7. metadata-eval 61.1%

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

   7. Simplified 61.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 17000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.92 \cdot 10^{+136}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* (* t a) -4.0) (* 27.0 (* j k)))))
   (if (<= j -1.1e+155)
     t_1
     (if (<= j -1.92e+136)
       (* -18.0 (* t (* x (* y (- z)))))
       (if (<= j -9e+120) t_1 (- (* b c) (* 4.0 (+ (* x i) (* t a)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	double tmp;
	if (j <= -1.1e+155) {
		tmp = t_1;
	} else if (j <= -1.92e+136) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if (j <= -9e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) * (-4.0d0)) - (27.0d0 * (j * k))
    if (j <= (-1.1d+155)) then
        tmp = t_1
    else if (j <= (-1.92d+136)) then
        tmp = (-18.0d0) * (t * (x * (y * -z)))
    else if (j <= (-9d+120)) then
        tmp = t_1
    else
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	double tmp;
	if (j <= -1.1e+155) {
		tmp = t_1;
	} else if (j <= -1.92e+136) {
		tmp = -18.0 * (t * (x * (y * -z)));
	} else if (j <= -9e+120) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((t * a) * -4.0) - (27.0 * (j * k))
	tmp = 0
	if j <= -1.1e+155:
		tmp = t_1
	elif j <= -1.92e+136:
		tmp = -18.0 * (t * (x * (y * -z)))
	elif j <= -9e+120:
		tmp = t_1
	else:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(t * a) * -4.0) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (j <= -1.1e+155)
		tmp = t_1;
	elseif (j <= -1.92e+136)
		tmp = Float64(-18.0 * Float64(t * Float64(x * Float64(y * Float64(-z)))));
	elseif (j <= -9e+120)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((t * a) * -4.0) - (27.0 * (j * k));
	tmp = 0.0;
	if (j <= -1.1e+155)
		tmp = t_1;
	elseif (j <= -1.92e+136)
		tmp = -18.0 * (t * (x * (y * -z)));
	elseif (j <= -9e+120)
		tmp = t_1;
	else
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.1e+155], t$95$1, If[LessEqual[j, -1.92e+136], N[(-18.0 * N[(t * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9e+120], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.1000000000000001e155 or -1.91999999999999998e136 < j < -8.99999999999999953e120

   1. Initial program 75.3%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x around 0 72.8%

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

   6. Taylor expanded in b around 0 67.3%

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

   if -1.1000000000000001e155 < j < -1.91999999999999998e136

   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 33.3%

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

      1. pow1 33.3%

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

      2. associate-*l* 33.3%

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

      3. associate-*r* 33.3%

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

   6. Applied egg-rr 33.3%

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

      1. unpow1 33.3%

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

      2. *-commutative 33.3%

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

   8. Simplified 33.3%

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

   9. Taylor expanded in x around -inf 34.5%

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

       1. mul-1-neg 34.5%

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

       2. cancel-sign-sub-inv 34.5%

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

       3. associate-*r* 34.5%

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

       4. metadata-eval 34.5%

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

   11. Simplified 34.5%

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

   12. Taylor expanded in t around inf 67.0%

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

   if -8.99999999999999953e120 < j

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0 78.0%

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

      1. distribute-lft-out 78.0%

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

      2. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in j around 0 67.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.92 \cdot 10^{+136}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+120}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-64} \lor \neg \left(t \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.25e-64) (not (<= t 1.3e+14)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.25e-64) || !(t <= 1.3e+14)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.25d-64)) .or. (.not. (t <= 1.3d+14))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.25e-64) || !(t <= 1.3e+14)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.25e-64) or not (t <= 1.3e+14):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.25e-64) || !(t <= 1.3e+14))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.25e-64) || ~((t <= 1.3e+14)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.25e-64], N[Not[LessEqual[t, 1.3e+14]], $MachinePrecision]], 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[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000008e-64 or 1.3e14 < t

   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 92.8%

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

      1. pow1 92.8%

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

      2. associate-*l* 92.7%

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

      3. associate-*r* 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. unpow1 92.7%

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

      2. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in i around 0 87.7%

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

   10. Taylor expanded in j around 0 84.9%

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

   if -1.25000000000000008e-64 < t < 1.3e14

   1. Initial program 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in t around 0 83.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-64} \lor \neg \left(t \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-22} \lor \neg \left(t \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.6e-22) (not (<= t 1.38e+14)))
   (* t (- (* a (- 4.0)) (* (* x (* y z)) -18.0)))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.6e-22) || !(t <= 1.38e+14)) {
		tmp = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-3.6d-22)) .or. (.not. (t <= 1.38d+14))) then
        tmp = t * ((a * -4.0d0) - ((x * (y * z)) * (-18.0d0)))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.6e-22) || !(t <= 1.38e+14)) {
		tmp = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3.6e-22) or not (t <= 1.38e+14):
		tmp = t * ((a * -4.0) - ((x * (y * z)) * -18.0))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.6e-22) || !(t <= 1.38e+14))
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(x * Float64(y * z)) * -18.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -3.6e-22) || ~((t <= 1.38e+14)))
		tmp = t * ((a * -4.0) - ((x * (y * z)) * -18.0));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.6e-22], N[Not[LessEqual[t, 1.38e+14]], $MachinePrecision]], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999998e-22 or 1.38e14 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in t around -inf 75.9%

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

      1. associate-*r* 75.9%

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

      2. neg-mul-1 75.9%

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

      3. cancel-sign-sub-inv 75.9%

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

      4. metadata-eval 75.9%

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

      5. *-commutative 75.9%

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

      6. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -3.5999999999999998e-22 < t < 1.38e14

   1. Initial program 80.9%

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

   3. Simplified 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. Taylor expanded in t around 0 82.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-22} \lor \neg \left(t \leq 1.38 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-193}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* a (* t -4.0))))
   (if (<= t -5.8e+18)
     t_1
     (if (<= t 6e-193)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= t 5.5e+125) (- (* b c) (* x (* 4.0 i))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if (t <= -5.8e+18) {
		tmp = t_1;
	} else if (t <= 6e-193) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 5.5e+125) {
		tmp = (b * c) - (x * (4.0 * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * (-4.0d0))
    if (t <= (-5.8d+18)) then
        tmp = t_1
    else if (t <= 6d-193) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 5.5d+125) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double tmp;
	if (t <= -5.8e+18) {
		tmp = t_1;
	} else if (t <= 6e-193) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 5.5e+125) {
		tmp = (b * c) - (x * (4.0 * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (t * -4.0)
	tmp = 0
	if t <= -5.8e+18:
		tmp = t_1
	elif t <= 6e-193:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 5.5e+125:
		tmp = (b * c) - (x * (4.0 * i))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (t <= -5.8e+18)
		tmp = t_1;
	elseif (t <= 6e-193)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 5.5e+125)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (t * -4.0);
	tmp = 0.0;
	if (t <= -5.8e+18)
		tmp = t_1;
	elseif (t <= 6e-193)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 5.5e+125)
		tmp = (b * c) - (x * (4.0 * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+18], t$95$1, If[LessEqual[t, 6e-193], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+125], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8e18 or 5.49999999999999996e125 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0 66.0%

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

      1. distribute-lft-out 66.0%

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

      2. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in t around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

   8. Simplified 45.3%

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

   if -5.8e18 < t < 5.9999999999999998e-193

   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 79.2%

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

   5. Taylor expanded in x around 0 73.0%

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

   6. Taylor expanded in a around 0 67.0%

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

   if 5.9999999999999998e-193 < t < 5.49999999999999996e125

   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 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. Taylor expanded in t around 0 67.1%

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

   6. Taylor expanded in i around inf 56.1%

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

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-193}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.6 \cdot 10^{+44} \lor \neg \left(b \cdot c \leq 8.4 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -7.6e+44) (not (<= (* b c) 8.4e+48)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -7.6e+44) || !((b * c) <= 8.4e+48)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-7.6d+44)) .or. (.not. ((b * c) <= 8.4d+48))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -7.6e+44) || !((b * c) <= 8.4e+48)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -7.6e+44) or not ((b * c) <= 8.4e+48):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -7.6e+44) || !(Float64(b * c) <= 8.4e+48))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -7.6e+44) || ~(((b * c) <= 8.4e+48)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -7.6e+44], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.4e+48]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -7.6000000000000004e44 or 8.3999999999999994e48 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 84.2%

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

      1. pow1 84.2%

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

      2. associate-*l* 84.2%

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

      3. associate-*r* 84.2%

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

   6. Applied egg-rr 84.2%

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

      1. unpow1 84.2%

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

      2. *-commutative 84.2%

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

   8. Simplified 84.2%

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

   9. Taylor expanded in b around inf 50.9%

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

   if -7.6000000000000004e44 < (*.f64 b c) < 8.3999999999999994e48

   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 89.5%

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

   5. Taylor expanded in j around inf 27.4%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.6 \cdot 10^{+44} \lor \neg \left(b \cdot c \leq 8.4 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+18} \lor \neg \left(t \leq 1.45 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.5e+18) (not (<= t 1.45e+125)))
   (* a (* t -4.0))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+18) || !(t <= 1.45e+125)) {
		tmp = a * (t * -4.0);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-7.5d+18)) .or. (.not. (t <= 1.45d+125))) then
        tmp = a * (t * (-4.0d0))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+18) || !(t <= 1.45e+125)) {
		tmp = a * (t * -4.0);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.5e+18) or not (t <= 1.45e+125):
		tmp = a * (t * -4.0)
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.5e+18) || !(t <= 1.45e+125))
		tmp = Float64(a * Float64(t * -4.0));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.5e+18) || ~((t <= 1.45e+125)))
		tmp = a * (t * -4.0);
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.5e+18], N[Not[LessEqual[t, 1.45e+125]], $MachinePrecision]], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e18 or 1.44999999999999997e125 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0 66.0%

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

      1. distribute-lft-out 66.0%

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

      2. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in t around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

   8. Simplified 45.3%

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

   if -7.5e18 < t < 1.44999999999999997e125

   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 84.2%

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

   5. Taylor expanded in b around inf 57.9%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+18} \lor \neg \left(t \leq 1.45 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 45.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+18} \lor \neg \left(t \leq 3.55 \cdot 10^{+124}\right):\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.5e+18) (not (<= t 3.55e+124)))
   (* a (* t -4.0))
   (- (* 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+18) || !(t <= 3.55e+124)) {
		tmp = a * (t * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-7.5d+18)) .or. (.not. (t <= 3.55d+124))) then
        tmp = a * (t * (-4.0d0))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+18) || !(t <= 3.55e+124)) {
		tmp = a * (t * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.5e+18) or not (t <= 3.55e+124):
		tmp = a * (t * -4.0)
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.5e+18) || !(t <= 3.55e+124))
		tmp = Float64(a * Float64(t * -4.0));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.5e+18) || ~((t <= 3.55e+124)))
		tmp = a * (t * -4.0);
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.5e+18], N[Not[LessEqual[t, 3.55e+124]], $MachinePrecision]], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e18 or 3.5500000000000002e124 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0 66.0%

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

      1. distribute-lft-out 66.0%

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

      2. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in t around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

   8. Simplified 45.3%

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

   if -7.5e18 < t < 3.5500000000000002e124

   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 83.6%

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

   5. Taylor expanded in x around 0 65.3%

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

   6. Taylor expanded in a around 0 58.0%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+18} \lor \neg \left(t \leq 3.55 \cdot 10^{+124}\right):\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.3% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 87.1%

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

   1. pow1 87.1%

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

   2. associate-*l* 87.1%

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

   3. associate-*r* 87.1%

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

6. Applied egg-rr 87.1%

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

   1. unpow1 87.1%

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

   2. *-commutative 87.1%

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

8. Simplified 87.1%

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

9. Taylor expanded in b around inf 25.4%

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

10. Final simplification 25.4%

    \[\leadsto b \cdot c \]
11. Add Preprocessing

Developer target: 89.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(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)))