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

Percentage Accurate: 85.2% → 90.1%

Time: 20.6s

Alternatives: 25

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: 85.2% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\mathsf{fma}\left(18, \left(t \cdot x\right) \cdot z, b \cdot \frac{c}{y}\right) - \mathsf{fma}\left(4, a \cdot \frac{t}{y}, \mathsf{fma}\left(4, i \cdot \frac{x}{y}, \left(j \cdot \frac{k}{y}\right) \cdot 27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.2e+104)
   (*
    y
    (-
     (fma 18.0 (* (* t x) z) (* b (/ c y)))
     (fma 4.0 (* a (/ t y)) (fma 4.0 (* i (/ x y)) (* (* j (/ k y)) 27.0)))))
   (-
    (-
     (+ (- (* t (* z (* y (* 18.0 x)))) (* t (* 4.0 a))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.2e+104) {
		tmp = y * (fma(18.0, ((t * x) * z), (b * (c / y))) - fma(4.0, (a * (t / y)), fma(4.0, (i * (x / y)), ((j * (k / y)) * 27.0))));
	} else {
		tmp = ((((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.2e+104)
		tmp = Float64(y * Float64(fma(18.0, Float64(Float64(t * x) * z), Float64(b * Float64(c / y))) - fma(4.0, Float64(a * Float64(t / y)), fma(4.0, Float64(i * Float64(x / y)), Float64(Float64(j * Float64(k / y)) * 27.0)))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(4.0 * a))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.2e+104], N[(y * N[(N[(18.0 * N[(N[(t * x), $MachinePrecision] * z), $MachinePrecision] + N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(i * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(k / y), $MachinePrecision]), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e104

   1. Initial program 68.5%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in y around inf 89.3%

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

      1. sub-neg 89.3%

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

      2. +-commutative 89.3%

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

      3. metadata-eval 89.3%

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

      4. cancel-sign-sub-inv 89.3%

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

      5. sub-neg 89.3%

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

      6. associate--r+ 89.3%

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

   7. Simplified 95.6%

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

   if -1.2e104 < y

   1. Initial program 87.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(\mathsf{fma}\left(18, \left(t \cdot x\right) \cdot z, b \cdot \frac{c}{y}\right) - \mathsf{fma}\left(4, a \cdot \frac{t}{y}, \mathsf{fma}\left(4, i \cdot \frac{x}{y}, \left(j \cdot \frac{k}{y}\right) \cdot 27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $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 97.4%

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

   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 28.6%

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

   5. Taylor expanded in a around 0 25.9%

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

   6. Taylor expanded in b around 0 28.6%

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

   7. Taylor expanded in x around inf 65.9%

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

      1. cancel-sign-sub-inv 65.9%

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

      2. associate-*r* 65.9%

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

      3. *-commutative 65.9%

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

      4. metadata-eval 65.9%

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

      5. *-commutative 65.9%

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

   9. Simplified 65.9%

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

4. Final simplification 93.1%

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

Alternative 3: 69.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;t\_3 \leq 200000000000:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+48}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(t\_2 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a))))
        (t_2 (* 4.0 (* x i)))
        (t_3 (* k (* j 27.0))))
   (if (<= t_3 -1e-15)
     (- (* b c) (* k (+ (* j 27.0) (* 4.0 (/ (* x i) k)))))
     (if (<= t_3 200000000000.0)
       (- t_1 t_2)
       (if (<= t_3 5e+48)
         (- (* 18.0 (* t (* x (* y z)))) (+ t_2 (* 27.0 (* j k))))
         (- t_1 t_3))))))

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 * (t * a));
	double t_2 = 4.0 * (x * i);
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e-15) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else if (t_3 <= 200000000000.0) {
		tmp = t_1 - t_2;
	} else if (t_3 <= 5e+48) {
		tmp = (18.0 * (t * (x * (y * z)))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = t_1 - t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = 4.0d0 * (x * i)
    t_3 = k * (j * 27.0d0)
    if (t_3 <= (-1d-15)) then
        tmp = (b * c) - (k * ((j * 27.0d0) + (4.0d0 * ((x * i) / k))))
    else if (t_3 <= 200000000000.0d0) then
        tmp = t_1 - t_2
    else if (t_3 <= 5d+48) then
        tmp = (18.0d0 * (t * (x * (y * z)))) - (t_2 + (27.0d0 * (j * k)))
    else
        tmp = t_1 - t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = 4.0 * (x * i);
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e-15) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else if (t_3 <= 200000000000.0) {
		tmp = t_1 - t_2;
	} else if (t_3 <= 5e+48) {
		tmp = (18.0 * (t * (x * (y * z)))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = t_1 - t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = 4.0 * (x * i)
	t_3 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -1e-15:
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))))
	elif t_3 <= 200000000000.0:
		tmp = t_1 - t_2
	elif t_3 <= 5e+48:
		tmp = (18.0 * (t * (x * (y * z)))) - (t_2 + (27.0 * (j * k)))
	else:
		tmp = t_1 - t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -1e-15)
		tmp = Float64(Float64(b * c) - Float64(k * Float64(Float64(j * 27.0) + Float64(4.0 * Float64(Float64(x * i) / k)))));
	elseif (t_3 <= 200000000000.0)
		tmp = Float64(t_1 - t_2);
	elseif (t_3 <= 5e+48)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) - Float64(t_2 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t_1 - t_3);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = 4.0 * (x * i);
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -1e-15)
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	elseif (t_3 <= 200000000000.0)
		tmp = t_1 - t_2;
	elseif (t_3 <= 5e+48)
		tmp = (18.0 * (t * (x * (y * z)))) - (t_2 + (27.0 * (j * k)));
	else
		tmp = t_1 - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-15], N[(N[(b * c), $MachinePrecision] - N[(k * N[(N[(j * 27.0), $MachinePrecision] + N[(4.0 * N[(N[(x * i), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 200000000000.0], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 5e+48], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e-15

   1. Initial program 74.2%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around 0 70.5%

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

   6. Taylor expanded in k around inf 72.2%

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

   if -1.0000000000000001e-15 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e11

   1. Initial program 87.1%

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

      1. distribute-rgt-out-- 90.0%

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

      2. associate-*r* 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.0%

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

      5. associate-*r* 88.0%

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

   4. Applied egg-rr 88.0%

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

   5. Taylor expanded in y around 0 80.3%

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

   6. Taylor expanded in j around 0 78.9%

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

   if 2e11 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999973e48

   1. Initial program 87.7%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 99.6%

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

   6. Taylor expanded in b around 0 99.6%

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

   if 4.99999999999999973e48 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 87.6%

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

      1. distribute-rgt-out-- 89.7%

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

      2. associate-*r* 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l* 89.7%

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

      5. associate-*r* 89.7%

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

   4. Applied egg-rr 89.7%

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

   5. Taylor expanded in x around 0 75.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 200000000000:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+48}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right) + t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-286}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (- (* 4.0 (- a)) (* (* y x) (* z -18.0))))))
   (if (<= t -4.3e-5)
     t_2
     (if (<= t -5.5e-86)
       (+ (* 18.0 (* (* t x) (* y z))) t_1)
       (if (<= t 2.8e-286)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= t 1.6e-214)
           (- (* b c) (* 27.0 (* j k)))
           (if (<= t 1e+41) (+ t_1 (* -4.0 (* x i))) 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 = j * (k * -27.0);
	double t_2 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	double tmp;
	if (t <= -4.3e-5) {
		tmp = t_2;
	} else if (t <= -5.5e-86) {
		tmp = (18.0 * ((t * x) * (y * z))) + t_1;
	} else if (t <= 2.8e-286) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.6e-214) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1e+41) {
		tmp = t_1 + (-4.0 * (x * i));
	} 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 = j * (k * (-27.0d0))
    t_2 = t * ((4.0d0 * -a) - ((y * x) * (z * (-18.0d0))))
    if (t <= (-4.3d-5)) then
        tmp = t_2
    else if (t <= (-5.5d-86)) then
        tmp = (18.0d0 * ((t * x) * (y * z))) + t_1
    else if (t <= 2.8d-286) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 1.6d-214) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 1d+41) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    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 = j * (k * -27.0);
	double t_2 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	double tmp;
	if (t <= -4.3e-5) {
		tmp = t_2;
	} else if (t <= -5.5e-86) {
		tmp = (18.0 * ((t * x) * (y * z))) + t_1;
	} else if (t <= 2.8e-286) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.6e-214) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1e+41) {
		tmp = t_1 + (-4.0 * (x * i));
	} 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 = j * (k * -27.0)
	t_2 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)))
	tmp = 0
	if t <= -4.3e-5:
		tmp = t_2
	elif t <= -5.5e-86:
		tmp = (18.0 * ((t * x) * (y * z))) + t_1
	elif t <= 2.8e-286:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 1.6e-214:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 1e+41:
		tmp = t_1 + (-4.0 * (x * i))
	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(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(4.0 * Float64(-a)) - Float64(Float64(y * x) * Float64(z * -18.0))))
	tmp = 0.0
	if (t <= -4.3e-5)
		tmp = t_2;
	elseif (t <= -5.5e-86)
		tmp = Float64(Float64(18.0 * Float64(Float64(t * x) * Float64(y * z))) + t_1);
	elseif (t <= 2.8e-286)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 1.6e-214)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1e+41)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	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 = j * (k * -27.0);
	t_2 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	tmp = 0.0;
	if (t <= -4.3e-5)
		tmp = t_2;
	elseif (t <= -5.5e-86)
		tmp = (18.0 * ((t * x) * (y * z))) + t_1;
	elseif (t <= 2.8e-286)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 1.6e-214)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 1e+41)
		tmp = t_1 + (-4.0 * (x * i));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(4.0 * (-a)), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] * N[(z * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e-5], t$95$2, If[LessEqual[t, -5.5e-86], N[(N[(18.0 * N[(N[(t * x), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 2.8e-286], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-214], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+41], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.3000000000000002e-5 or 1.00000000000000001e41 < t

   1. Initial program 84.5%

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

   3. Taylor expanded in t around -inf 65.5%

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

      1. associate-*r* 65.5%

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

      2. neg-mul-1 65.5%

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

      3. cancel-sign-sub-inv 65.5%

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

      4. metadata-eval 65.5%

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

      5. *-commutative 65.5%

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

      6. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in x around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-*r* 65.5%

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

      3. associate-*l* 65.5%

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

      4. associate-*r* 66.3%

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

   8. Simplified 66.3%

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

   if -4.3000000000000002e-5 < t < -5.5e-86

   1. Initial program 93.4%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in y around inf 57.8%

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

      1. associate-*r* 64.2%

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

   7. Simplified 64.2%

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

   if -5.5e-86 < t < 2.8e-286

   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 71.9%

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

   5. Taylor expanded in t around 0 81.5%

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

   6. Taylor expanded in i around inf 79.8%

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

      1. associate-*r* 79.8%

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

      2. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if 2.8e-286 < t < 1.60000000000000007e-214

   1. Initial program 87.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 87.8%

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

   6. Taylor expanded in i around 0 94.0%

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

   if 1.60000000000000007e-214 < t < 1.00000000000000001e41

   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 89.7%

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

   5. Taylor expanded in i around inf 57.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-286}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-88}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-72}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(y \cdot 18\right)\right) - 4 \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4e-88)
   (-
    (+ (* b c) (* t (- (* (* 18.0 x) (* y z)) (* 4.0 a))))
    (+ (* x (* 4.0 i)) (* j (* k 27.0))))
   (if (<= t 1.95e-72)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (-
      (-
       (+ (* b c) (* t (- (* x (* z (* y 18.0))) (* 4.0 a))))
       (* i (* x 4.0)))
      (* k (* j 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -4e-88) {
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (j * (k * 27.0)));
	} else if (t <= 1.95e-72) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = (((b * c) + (t * ((x * (z * (y * 18.0))) - (4.0 * a)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-4d-88)) then
        tmp = ((b * c) + (t * (((18.0d0 * x) * (y * z)) - (4.0d0 * a)))) - ((x * (4.0d0 * i)) + (j * (k * 27.0d0)))
    else if (t <= 1.95d-72) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = (((b * c) + (t * ((x * (z * (y * 18.0d0))) - (4.0d0 * a)))) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4e-88) {
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (j * (k * 27.0)));
	} else if (t <= 1.95e-72) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = (((b * c) + (t * ((x * (z * (y * 18.0))) - (4.0 * a)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -4e-88:
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (j * (k * 27.0)))
	elif t <= 1.95e-72:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = (((b * c) + (t * ((x * (z * (y * 18.0))) - (4.0 * a)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4e-88)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(18.0 * x) * Float64(y * z)) - Float64(4.0 * a)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(k * 27.0))));
	elseif (t <= 1.95e-72)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(y * 18.0))) - Float64(4.0 * a)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -4e-88)
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (j * (k * 27.0)));
	elseif (t <= 1.95e-72)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = (((b * c) + (t * ((x * (z * (y * 18.0))) - (4.0 * a)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4e-88], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-72], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(y * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999974e-88

   1. Initial program 88.5%

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

   3. Simplified 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

   if -3.99999999999999974e-88 < t < 1.95e-72

   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 78.0%

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

   5. Taylor expanded in y around 0 86.2%

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

   if 1.95e-72 < t

   1. Initial program 83.2%

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

      1. distribute-rgt-out-- 87.4%

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

      2. associate-*r* 88.8%

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

      3. *-commutative 88.8%

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

      4. associate-*l* 88.8%

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

      5. associate-*r* 88.8%

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

   4. Applied egg-rr 88.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-88}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-72}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(y \cdot 18\right)\right) - 4 \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+292}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* k (* j 27.0)) -1e+292)
   (- (* b c) (* k (+ (* j 27.0) (* 4.0 (/ (* x i) k)))))
   (-
    (+ (* b c) (* t (- (* (* 18.0 x) (* y z)) (* 4.0 a))))
    (+ (* x (* 4.0 i)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k * (j * 27.0)) <= -1e+292) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else {
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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 ((k * (j * 27.0d0)) <= (-1d+292)) then
        tmp = (b * c) - (k * ((j * 27.0d0) + (4.0d0 * ((x * i) / k))))
    else
        tmp = ((b * c) + (t * (((18.0d0 * x) * (y * z)) - (4.0d0 * a)))) - ((x * (4.0d0 * i)) + (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 ((k * (j * 27.0)) <= -1e+292) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else {
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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 (k * (j * 27.0)) <= -1e+292:
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))))
	else:
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (j * (k * 27.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(k * Float64(j * 27.0)) <= -1e+292)
		tmp = Float64(Float64(b * c) - Float64(k * Float64(Float64(j * 27.0) + Float64(4.0 * Float64(Float64(x * i) / k)))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(18.0 * x) * Float64(y * z)) - Float64(4.0 * a)))) - Float64(Float64(x * Float64(4.0 * i)) + 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 ((k * (j * 27.0)) <= -1e+292)
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	else
		tmp = ((b * c) + (t * (((18.0 * x) * (y * z)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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[LessEqual[N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision], -1e+292], N[(N[(b * c), $MachinePrecision] - N[(k * N[(N[(j * 27.0), $MachinePrecision] + N[(4.0 * N[(N[(x * i), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e292

   1. Initial program 47.1%

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

   3. Simplified 41.8%

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

   5. Taylor expanded in t around 0 59.4%

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

   6. Taylor expanded in k around inf 71.2%

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

   if -1e292 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.7%

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

   3. Simplified 89.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+292}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-283}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (- (* 4.0 (- a)) (* (* y x) (* z -18.0))))))
   (if (<= t -2.9e-87)
     t_1
     (if (<= t 1.7e-283)
       (- (* b c) (* x (* 4.0 i)))
       (if (<= t 5.4e-222)
         (- (* b c) (* 27.0 (* j k)))
         (if (<= t 1e+41) (+ (* j (* k -27.0)) (* -4.0 (* x 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 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	double tmp;
	if (t <= -2.9e-87) {
		tmp = t_1;
	} else if (t <= 1.7e-283) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 5.4e-222) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1e+41) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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 = t * ((4.0d0 * -a) - ((y * x) * (z * (-18.0d0))))
    if (t <= (-2.9d-87)) then
        tmp = t_1
    else if (t <= 1.7d-283) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 5.4d-222) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 1d+41) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * 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 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	double tmp;
	if (t <= -2.9e-87) {
		tmp = t_1;
	} else if (t <= 1.7e-283) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 5.4e-222) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1e+41) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)))
	tmp = 0
	if t <= -2.9e-87:
		tmp = t_1
	elif t <= 1.7e-283:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 5.4e-222:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 1e+41:
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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(t * Float64(Float64(4.0 * Float64(-a)) - Float64(Float64(y * x) * Float64(z * -18.0))))
	tmp = 0.0
	if (t <= -2.9e-87)
		tmp = t_1;
	elseif (t <= 1.7e-283)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 5.4e-222)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1e+41)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * 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 = t * ((4.0 * -a) - ((y * x) * (z * -18.0)));
	tmp = 0.0;
	if (t <= -2.9e-87)
		tmp = t_1;
	elseif (t <= 1.7e-283)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 5.4e-222)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 1e+41)
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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[(t * N[(N[(4.0 * (-a)), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] * N[(z * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-87], t$95$1, If[LessEqual[t, 1.7e-283], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-222], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+41], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8999999999999999e-87 or 1.00000000000000001e41 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in t around -inf 61.6%

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

      1. associate-*r* 61.6%

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

      2. neg-mul-1 61.6%

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

      3. cancel-sign-sub-inv 61.6%

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

      4. metadata-eval 61.6%

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

      5. *-commutative 61.6%

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

      6. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in x around 0 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*r* 61.6%

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

      3. associate-*l* 61.6%

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

      4. associate-*r* 62.3%

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

   8. Simplified 62.3%

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

   if -2.8999999999999999e-87 < t < 1.6999999999999999e-283

   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 71.9%

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

   5. Taylor expanded in t around 0 81.5%

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

   6. Taylor expanded in i around inf 79.8%

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

      1. associate-*r* 79.8%

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

      2. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if 1.6999999999999999e-283 < t < 5.4e-222

   1. Initial program 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around 0 93.2%

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

   6. Taylor expanded in i around 0 99.9%

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

   if 5.4e-222 < t < 1.00000000000000001e41

   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 88.2%

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

   5. Taylor expanded in i around inf 56.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-283}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (* i -4.0)))))
   (if (<= x -9.2e+82)
     t_1
     (if (<= x -1.85e+34)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= x -6e-225)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 2.8e+48) (- (* b c) (* 27.0 (* j k))) 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)) + (i * -4.0));
	double tmp;
	if (x <= -9.2e+82) {
		tmp = t_1;
	} else if (x <= -1.85e+34) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= -6e-225) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.8e+48) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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)) + (i * (-4.0d0)))
    if (x <= (-9.2d+82)) then
        tmp = t_1
    else if (x <= (-1.85d+34)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (x <= (-6d-225)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 2.8d+48) then
        tmp = (b * c) - (27.0d0 * (j * k))
    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)) + (i * -4.0));
	double tmp;
	if (x <= -9.2e+82) {
		tmp = t_1;
	} else if (x <= -1.85e+34) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= -6e-225) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.8e+48) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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)) + (i * -4.0))
	tmp = 0
	if x <= -9.2e+82:
		tmp = t_1
	elif x <= -1.85e+34:
		tmp = (b * c) + (j * (k * -27.0))
	elif x <= -6e-225:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 2.8e+48:
		tmp = (b * c) - (27.0 * (j * k))
	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(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -9.2e+82)
		tmp = t_1;
	elseif (x <= -1.85e+34)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -6e-225)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.8e+48)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	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)) + (i * -4.0));
	tmp = 0.0;
	if (x <= -9.2e+82)
		tmp = t_1;
	elseif (x <= -1.85e+34)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (x <= -6e-225)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 2.8e+48)
		tmp = (b * c) - (27.0 * (j * k));
	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[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+82], t$95$1, If[LessEqual[x, -1.85e+34], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-225], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+48], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.19999999999999953e82 or 2.80000000000000012e48 < x

   1. Initial program 73.0%

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

   3. Simplified 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 a around 0 72.4%

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

   6. Taylor expanded in b around 0 63.1%

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

   7. Taylor expanded in x around inf 73.2%

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

      1. cancel-sign-sub-inv 73.2%

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

      2. associate-*r* 73.2%

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

      3. *-commutative 73.2%

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

      4. metadata-eval 73.2%

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

      5. *-commutative 73.2%

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

   9. Simplified 73.2%

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

   if -9.19999999999999953e82 < x < -1.85000000000000004e34

   1. Initial program 72.3%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in b around inf 68.3%

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

   if -1.85000000000000004e34 < x < -6.00000000000000035e-225

   1. Initial program 92.7%

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

      1. distribute-rgt-out-- 94.5%

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

      2. associate-*r* 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-*l* 92.8%

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

      5. associate-*r* 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in y around 0 80.6%

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

   6. Taylor expanded in j around 0 71.9%

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

   7. Taylor expanded in i around 0 63.0%

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

   if -6.00000000000000035e-225 < x < 2.80000000000000012e48

   1. Initial program 94.0%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 67.9%

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

   6. Taylor expanded in i around 0 61.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+179}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18 \cdot t\right) \cdot \left(z \cdot \left(y \cdot x\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+139}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))))
   (if (<= z -8.2e+179)
     (-
      (- (+ (* b c) (* (* 18.0 t) (* z (* y x)))) (* i (* x 4.0)))
      (* k (* j 27.0)))
     (if (<= z 3.9e+139)
       (- (+ (* b c) (* -4.0 (* t a))) (+ t_1 (* 27.0 (* j k))))
       (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))) 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 = 4.0 * (x * i);
	double tmp;
	if (z <= -8.2e+179) {
		tmp = (((b * c) + ((18.0 * t) * (z * (y * x)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else if (z <= 3.9e+139) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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 = 4.0d0 * (x * i)
    if (z <= (-8.2d+179)) then
        tmp = (((b * c) + ((18.0d0 * t) * (z * (y * x)))) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    else if (z <= 3.9d+139) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (t_1 + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))) - 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 = 4.0 * (x * i);
	double tmp;
	if (z <= -8.2e+179) {
		tmp = (((b * c) + ((18.0 * t) * (z * (y * x)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else if (z <= 3.9e+139) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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 = 4.0 * (x * i)
	tmp = 0
	if z <= -8.2e+179:
		tmp = (((b * c) + ((18.0 * t) * (z * (y * x)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	elif z <= 3.9e+139:
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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(4.0 * Float64(x * i))
	tmp = 0.0
	if (z <= -8.2e+179)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(18.0 * t) * Float64(z * Float64(y * x)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	elseif (z <= 3.9e+139)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))) - 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 = 4.0 * (x * i);
	tmp = 0.0;
	if (z <= -8.2e+179)
		tmp = (((b * c) + ((18.0 * t) * (z * (y * x)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	elseif (z <= 3.9e+139)
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+179], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(18.0 * t), $MachinePrecision] * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+139], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000021e179

   1. Initial program 72.6%

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

      1. distribute-rgt-out-- 83.7%

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

      2. associate-*r* 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*l* 75.9%

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

      5. associate-*r* 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in x around inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. associate-*r* 73.6%

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

   7. Simplified 73.6%

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

   if -8.20000000000000021e179 < z < 3.90000000000000006e139

   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 90.7%

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

   5. Taylor expanded in y around 0 89.4%

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

   if 3.90000000000000006e139 < z

   1. Initial program 74.9%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in j around 0 68.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+179}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18 \cdot t\right) \cdot \left(z \cdot \left(y \cdot x\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+139}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-9}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e-15)
     (- (* b c) (* k (+ (* j 27.0) (* 4.0 (/ (* x i) k)))))
     (if (<= t_2 2e-9) (- t_1 (* 4.0 (* x i))) (- t_1 (* 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 t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e-15) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else if (t_2 <= 2e-9) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d-15)) then
        tmp = (b * c) - (k * ((j * 27.0d0) + (4.0d0 * ((x * i) / k))))
    else if (t_2 <= 2d-9) then
        tmp = t_1 - (4.0d0 * (x * i))
    else
        tmp = t_1 - (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 t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e-15) {
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	} else if (t_2 <= 2e-9) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = t_1 - (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):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e-15:
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))))
	elif t_2 <= 2e-9:
		tmp = t_1 - (4.0 * (x * i))
	else:
		tmp = t_1 - (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)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e-15)
		tmp = Float64(Float64(b * c) - Float64(k * Float64(Float64(j * 27.0) + Float64(4.0 * Float64(Float64(x * i) / k)))));
	elseif (t_2 <= 2e-9)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(t_1 - 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)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e-15)
		tmp = (b * c) - (k * ((j * 27.0) + (4.0 * ((x * i) / k))));
	elseif (t_2 <= 2e-9)
		tmp = t_1 - (4.0 * (x * i));
	else
		tmp = t_1 - (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_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-15], N[(N[(b * c), $MachinePrecision] - N[(k * N[(N[(j * 27.0), $MachinePrecision] + N[(4.0 * N[(N[(x * i), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-9], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e-15

   1. Initial program 74.2%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around 0 70.5%

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

   6. Taylor expanded in k around inf 72.2%

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

   if -1.0000000000000001e-15 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000012e-9

   1. Initial program 86.6%

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

      1. distribute-rgt-out-- 89.6%

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

      2. associate-*r* 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l* 87.6%

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

      5. associate-*r* 87.6%

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

   4. Applied egg-rr 87.6%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in j around 0 78.9%

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

   if 2.00000000000000012e-9 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 93.4%

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

   5. Taylor expanded in x around 0 72.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27 + 4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-321}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 7.8 \cdot 10^{+161}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= (* b c) -5e+85)
     t_1
     (if (<= (* b c) 1e-321)
       (* -4.0 (+ (* x i) (* t a)))
       (if (<= (* b c) 7.8e+161)
         (+ (* j (* k -27.0)) (* -4.0 (* x 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 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5e+85) {
		tmp = t_1;
	} else if ((b * c) <= 1e-321) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if ((b * c) <= 7.8e+161) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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 = (b * c) + ((-4.0d0) * (t * a))
    if ((b * c) <= (-5d+85)) then
        tmp = t_1
    else if ((b * c) <= 1d-321) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if ((b * c) <= 7.8d+161) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * 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 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5e+85) {
		tmp = t_1;
	} else if ((b * c) <= 1e-321) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if ((b * c) <= 7.8e+161) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -5e+85:
		tmp = t_1
	elif (b * c) <= 1e-321:
		tmp = -4.0 * ((x * i) + (t * a))
	elif (b * c) <= 7.8e+161:
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -5e+85)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-321)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (Float64(b * c) <= 7.8e+161)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * 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 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -5e+85)
		tmp = t_1;
	elseif ((b * c) <= 1e-321)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif ((b * c) <= 7.8e+161)
		tmp = (j * (k * -27.0)) + (-4.0 * (x * 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[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+85], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-321], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.8e+161], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.0000000000000001e85 or 7.8000000000000004e161 < (*.f64 b c)

   1. Initial program 77.4%

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

      1. distribute-rgt-out-- 80.6%

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

      2. associate-*r* 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*l* 79.5%

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

      5. associate-*r* 79.5%

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

   4. Applied egg-rr 79.5%

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

   5. Taylor expanded in y around 0 79.4%

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

   6. Taylor expanded in j around 0 79.1%

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

   7. Taylor expanded in i around 0 71.3%

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

   if -5.0000000000000001e85 < (*.f64 b c) < 9.98013e-322

   1. Initial program 86.1%

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

      1. distribute-rgt-out-- 88.2%

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

      2. associate-*r* 86.3%

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

      3. *-commutative 86.3%

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

      4. associate-*l* 86.3%

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

      5. associate-*r* 86.3%

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

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in y around 0 76.2%

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

   6. Taylor expanded in j around 0 59.5%

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

   7. Taylor expanded in b around 0 58.2%

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

      1. cancel-sign-sub-inv 58.2%

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

      2. metadata-eval 58.2%

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

      3. distribute-lft-out 58.2%

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

      4. *-commutative 58.2%

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

      5. *-commutative 58.2%

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

   9. Simplified 58.2%

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

   if 9.98013e-322 < (*.f64 b c) < 7.8000000000000004e161

   1. Initial program 90.8%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in i around inf 62.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-321}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 7.8 \cdot 10^{+161}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;4 \cdot a \leq -5 \cdot 10^{-29} \lor \neg \left(4 \cdot a \leq 10^{-29}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))))
   (if (or (<= (* 4.0 a) -5e-29) (not (<= (* 4.0 a) 1e-29)))
     (- (+ (* b c) (* -4.0 (* t a))) t_1)
     (- (* b c) (+ t_1 (* 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 t_1 = 4.0 * (x * i);
	double tmp;
	if (((4.0 * a) <= -5e-29) || !((4.0 * a) <= 1e-29)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = (b * c) - (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    if (((4.0d0 * a) <= (-5d-29)) .or. (.not. ((4.0d0 * a) <= 1d-29))) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else
        tmp = (b * c) - (t_1 + (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 t_1 = 4.0 * (x * i);
	double tmp;
	if (((4.0 * a) <= -5e-29) || !((4.0 * a) <= 1e-29)) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = (b * c) - (t_1 + (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):
	t_1 = 4.0 * (x * i)
	tmp = 0
	if ((4.0 * a) <= -5e-29) or not ((4.0 * a) <= 1e-29):
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	else:
		tmp = (b * c) - (t_1 + (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)
	t_1 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if ((Float64(4.0 * a) <= -5e-29) || !(Float64(4.0 * a) <= 1e-29))
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(t_1 + 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)
	t_1 = 4.0 * (x * i);
	tmp = 0.0;
	if (((4.0 * a) <= -5e-29) || ~(((4.0 * a) <= 1e-29)))
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	else
		tmp = (b * c) - (t_1 + (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_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(4.0 * a), $MachinePrecision], -5e-29], N[Not[LessEqual[N[(4.0 * a), $MachinePrecision], 1e-29]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -4.99999999999999986e-29 or 9.99999999999999943e-30 < (*.f64 a #s(literal 4 binary64))

   1. Initial program 82.4%

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

      1. distribute-rgt-out-- 86.9%

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

      2. associate-*r* 86.9%

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

      3. *-commutative 86.9%

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

      4. associate-*l* 86.9%

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

      5. associate-*r* 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in y around 0 78.0%

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

   6. Taylor expanded in j around 0 72.2%

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

   if -4.99999999999999986e-29 < (*.f64 a #s(literal 4 binary64)) < 9.99999999999999943e-30

   1. Initial program 85.9%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around 0 77.3%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;4 \cdot a \leq -5 \cdot 10^{-29} \lor \neg \left(4 \cdot a \leq 10^{-29}\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))))
   (if (<= z 4.2e+140)
     (- (+ (* b c) (* -4.0 (* t a))) (+ t_1 (* 27.0 (* j k))))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))) 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 = 4.0 * (x * i);
	double tmp;
	if (z <= 4.2e+140) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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 = 4.0d0 * (x * i)
    if (z <= 4.2d+140) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (t_1 + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))) - 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 = 4.0 * (x * i);
	double tmp;
	if (z <= 4.2e+140) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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 = 4.0 * (x * i)
	tmp = 0
	if z <= 4.2e+140:
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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(4.0 * Float64(x * i))
	tmp = 0.0
	if (z <= 4.2e+140)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))) - 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 = 4.0 * (x * i);
	tmp = 0.0;
	if (z <= 4.2e+140)
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_1 + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - 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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 4.2e+140], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 4.2000000000000004e140

   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 88.2%

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

   5. Taylor expanded in y around 0 83.1%

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

   if 4.2000000000000004e140 < z

   1. Initial program 74.9%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in j around 0 68.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5.2e+139)
   (* b c)
   (if (<= (* b c) -2.6e-272)
     (* -4.0 (* t a))
     (if (<= (* b c) 2.6e+21) (* (* j k) -27.0) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5.2e+139) {
		tmp = b * c;
	} else if ((b * c) <= -2.6e-272) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 2.6e+21) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-5.2d+139)) then
        tmp = b * c
    else if ((b * c) <= (-2.6d-272)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 2.6d+21) then
        tmp = (j * k) * (-27.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5.2e+139) {
		tmp = b * c;
	} else if ((b * c) <= -2.6e-272) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 2.6e+21) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5.2e+139:
		tmp = b * c
	elif (b * c) <= -2.6e-272:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 2.6e+21:
		tmp = (j * k) * -27.0
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5.2e+139)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.6e-272)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 2.6e+21)
		tmp = Float64(Float64(j * k) * -27.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5.2e+139)
		tmp = b * c;
	elseif ((b * c) <= -2.6e-272)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 2.6e+21)
		tmp = (j * k) * -27.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5.2e+139], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.6e-272], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.6e+21], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.20000000000000044e139 or 2.6e21 < (*.f64 b c)

   1. Initial program 79.4%

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

      1. distribute-rgt-out-- 82.2%

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

      2. associate-*r* 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*l* 82.2%

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

      5. associate-*r* 82.2%

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

   4. Applied egg-rr 82.2%

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

   5. Taylor expanded in b around inf 54.5%

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

   if -5.20000000000000044e139 < (*.f64 b c) < -2.59999999999999992e-272

   1. Initial program 87.2%

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

      1. distribute-rgt-out-- 90.1%

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

      2. associate-*r* 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l* 90.2%

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

      5. associate-*r* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in y around 0 79.4%

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

   6. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

   8. Simplified 31.9%

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

   if -2.59999999999999992e-272 < (*.f64 b c) < 2.6e21

   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 86.6%

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

   5. Taylor expanded in j around inf 35.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+21}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 77.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+256}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* 4.0 (* x i)) (* 27.0 (* j k)))))
   (if (<= y -8.8e+256)
     (- (* 18.0 (* t (* x (* y z)))) t_1)
     (- (+ (* b c) (* -4.0 (* t a))) 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 = (4.0 * (x * i)) + (27.0 * (j * k));
	double tmp;
	if (y <= -8.8e+256) {
		tmp = (18.0 * (t * (x * (y * z)))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 = (4.0d0 * (x * i)) + (27.0d0 * (j * k))
    if (y <= (-8.8d+256)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) - t_1
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - 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 = (4.0 * (x * i)) + (27.0 * (j * k));
	double tmp;
	if (y <= -8.8e+256) {
		tmp = (18.0 * (t * (x * (y * z)))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 = (4.0 * (x * i)) + (27.0 * (j * k))
	tmp = 0
	if y <= -8.8e+256:
		tmp = (18.0 * (t * (x * (y * z)))) - t_1
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - 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(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (y <= -8.8e+256)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - 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 = (4.0 * (x * i)) + (27.0 * (j * k));
	tmp = 0.0;
	if (y <= -8.8e+256)
		tmp = (18.0 * (t * (x * (y * z)))) - t_1;
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - 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[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e+256], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.7999999999999997e256

   1. Initial program 71.4%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in a around 0 78.6%

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

   6. Taylor expanded in b around 0 78.6%

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

   if -8.7999999999999997e256 < y

   1. Initial program 84.8%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around 0 81.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+256}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+83} \lor \neg \left(x \leq 5 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= x -1.08e+83) (not (<= x 5e+60)))
   (* x (+ (* (* 18.0 t) (* y z)) (* i -4.0)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 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 ((x <= -1.08e+83) || !(x <= 5e+60)) {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 ((x <= (-1.08d+83)) .or. (.not. (x <= 5d+60))) then
        tmp = x * (((18.0d0 * t) * (y * z)) + (i * (-4.0d0)))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (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 ((x <= -1.08e+83) || !(x <= 5e+60)) {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 (x <= -1.08e+83) or not (x <= 5e+60):
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 ((x <= -1.08e+83) || !(x <= 5e+60))
		tmp = Float64(x * Float64(Float64(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - 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 ((x <= -1.08e+83) || ~((x <= 5e+60)))
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (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[x, -1.08e+83], N[Not[LessEqual[x, 5e+60]], $MachinePrecision]], N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e83 or 4.99999999999999975e60 < x

   1. Initial program 73.4%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in a around 0 73.8%

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

   6. Taylor expanded in b around 0 64.3%

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

   7. Taylor expanded in x around inf 73.6%

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

      1. cancel-sign-sub-inv 73.6%

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

      2. associate-*r* 73.6%

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

      3. *-commutative 73.6%

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

      4. metadata-eval 73.6%

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

      5. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -1.08e83 < x < 4.99999999999999975e60

   1. Initial program 91.4%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 76.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+83} \lor \neg \left(x \leq 5 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \left(t\_1 - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t\_1 - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 4.0 (- a))))
   (if (<= t -1.4e+128)
     (* t (- t_1 (* (* x (* y z)) -18.0)))
     (if (<= t 2.1e+54)
       (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
       (* t (- t_1 (* (* y x) (* z -18.0))))))))

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 t_1 = 4.0 * -a;
	double tmp;
	if (t <= -1.4e+128) {
		tmp = t * (t_1 - ((x * (y * z)) * -18.0));
	} else if (t <= 2.1e+54) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (t_1 - ((y * x) * (z * -18.0)));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * -a
    if (t <= (-1.4d+128)) then
        tmp = t * (t_1 - ((x * (y * z)) * (-18.0d0)))
    else if (t <= 2.1d+54) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t * (t_1 - ((y * x) * (z * (-18.0d0))))
    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 t_1 = 4.0 * -a;
	double tmp;
	if (t <= -1.4e+128) {
		tmp = t * (t_1 - ((x * (y * z)) * -18.0));
	} else if (t <= 2.1e+54) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (t_1 - ((y * x) * (z * -18.0)));
	}
	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):
	t_1 = 4.0 * -a
	tmp = 0
	if t <= -1.4e+128:
		tmp = t * (t_1 - ((x * (y * z)) * -18.0))
	elif t <= 2.1e+54:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t * (t_1 - ((y * x) * (z * -18.0)))
	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)
	t_1 = Float64(4.0 * Float64(-a))
	tmp = 0.0
	if (t <= -1.4e+128)
		tmp = Float64(t * Float64(t_1 - Float64(Float64(x * Float64(y * z)) * -18.0)));
	elseif (t <= 2.1e+54)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t * Float64(t_1 - Float64(Float64(y * x) * Float64(z * -18.0))));
	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)
	t_1 = 4.0 * -a;
	tmp = 0.0;
	if (t <= -1.4e+128)
		tmp = t * (t_1 - ((x * (y * z)) * -18.0));
	elseif (t <= 2.1e+54)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t * (t_1 - ((y * x) * (z * -18.0)));
	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_] := Block[{t$95$1 = N[(4.0 * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.4e+128], N[(t * N[(t$95$1 - N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+54], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(t$95$1 - N[(N[(y * x), $MachinePrecision] * N[(z * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999991e128

   1. Initial program 85.6%

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

   3. Taylor expanded in t around -inf 80.7%

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

      1. associate-*r* 80.7%

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

      2. neg-mul-1 80.7%

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

      3. cancel-sign-sub-inv 80.7%

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

      4. metadata-eval 80.7%

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

      5. *-commutative 80.7%

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

      6. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   if -1.39999999999999991e128 < t < 2.09999999999999986e54

   1. Initial program 84.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in t around 0 72.2%

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

   if 2.09999999999999986e54 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in t around -inf 65.9%

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

      1. associate-*r* 65.9%

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

      2. neg-mul-1 65.9%

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

      3. cancel-sign-sub-inv 65.9%

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

      4. metadata-eval 65.9%

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

      5. *-commutative 65.9%

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

      6. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in x around 0 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*r* 65.9%

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

      3. associate-*l* 65.9%

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

      4. associate-*r* 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(4 \cdot \left(-a\right) - \left(y \cdot x\right) \cdot \left(z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+87} \lor \neg \left(b \cdot c \leq 7.5 \cdot 10^{+151}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* b c) -5.2e+87) (not (<= (* b c) 7.5e+151)))
   (+ (* b c) (* -4.0 (* t a)))
   (* -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 tmp;
	if (((b * c) <= -5.2e+87) || !((b * c) <= 7.5e+151)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = -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) :: tmp
    if (((b * c) <= (-5.2d+87)) .or. (.not. ((b * c) <= 7.5d+151))) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (-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 tmp;
	if (((b * c) <= -5.2e+87) || !((b * c) <= 7.5e+151)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = -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):
	tmp = 0
	if ((b * c) <= -5.2e+87) or not ((b * c) <= 7.5e+151):
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = -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)
	tmp = 0.0
	if ((Float64(b * c) <= -5.2e+87) || !(Float64(b * c) <= 7.5e+151))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = 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)
	tmp = 0.0;
	if (((b * c) <= -5.2e+87) || ~(((b * c) <= 7.5e+151)))
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = -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_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -5.2e+87], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.5e+151]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.19999999999999997e87 or 7.49999999999999977e151 < (*.f64 b c)

   1. Initial program 77.9%

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

      1. distribute-rgt-out-- 81.0%

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

      2. associate-*r* 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*l* 79.9%

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

      5. associate-*r* 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in y around 0 79.8%

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

   6. Taylor expanded in j around 0 78.5%

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

   7. Taylor expanded in i around 0 70.8%

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

   if -5.19999999999999997e87 < (*.f64 b c) < 7.49999999999999977e151

   1. Initial program 87.9%

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

      1. distribute-rgt-out-- 89.8%

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

      2. associate-*r* 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*l* 89.4%

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

      5. associate-*r* 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in y around 0 78.2%

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

   6. Taylor expanded in j around 0 56.7%

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

   7. Taylor expanded in b around 0 53.6%

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

      1. cancel-sign-sub-inv 53.6%

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

      2. metadata-eval 53.6%

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

      3. distribute-lft-out 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   9. Simplified 53.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+87} \lor \neg \left(b \cdot c \leq 7.5 \cdot 10^{+151}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.16 \cdot 10^{+244} \lor \neg \left(b \cdot c \leq 4.7 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* b c) -1.16e+244) (not (<= (* b c) 4.7e+232)))
   (* 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 tmp;
	if (((b * c) <= -1.16e+244) || !((b * c) <= 4.7e+232)) {
		tmp = b * c;
	} else {
		tmp = -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) :: tmp
    if (((b * c) <= (-1.16d+244)) .or. (.not. ((b * c) <= 4.7d+232))) then
        tmp = b * c
    else
        tmp = (-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 tmp;
	if (((b * c) <= -1.16e+244) || !((b * c) <= 4.7e+232)) {
		tmp = b * c;
	} else {
		tmp = -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):
	tmp = 0
	if ((b * c) <= -1.16e+244) or not ((b * c) <= 4.7e+232):
		tmp = b * c
	else:
		tmp = -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)
	tmp = 0.0
	if ((Float64(b * c) <= -1.16e+244) || !(Float64(b * c) <= 4.7e+232))
		tmp = Float64(b * c);
	else
		tmp = 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)
	tmp = 0.0;
	if (((b * c) <= -1.16e+244) || ~(((b * c) <= 4.7e+232)))
		tmp = b * c;
	else
		tmp = -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_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.16e+244], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4.7e+232]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.16000000000000003e244 or 4.69999999999999992e232 < (*.f64 b c)

   1. Initial program 75.0%

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

      1. distribute-rgt-out-- 76.9%

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

      2. associate-*r* 75.0%

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

      3. *-commutative 75.0%

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

      4. associate-*l* 75.0%

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

      5. associate-*r* 75.0%

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

   4. Applied egg-rr 75.0%

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

   5. Taylor expanded in b around inf 79.2%

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

   if -1.16000000000000003e244 < (*.f64 b c) < 4.69999999999999992e232

   1. Initial program 86.4%

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

      1. distribute-rgt-out-- 88.9%

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

      2. associate-*r* 88.5%

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

      3. *-commutative 88.5%

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

      4. associate-*l* 88.5%

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

      5. associate-*r* 88.5%

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

   4. Applied egg-rr 88.5%

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

   5. Taylor expanded in y around 0 80.2%

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

   6. Taylor expanded in j around 0 61.7%

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

   7. Taylor expanded in b around 0 52.6%

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

      1. cancel-sign-sub-inv 52.6%

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

      2. metadata-eval 52.6%

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

      3. distribute-lft-out 52.6%

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

      4. *-commutative 52.6%

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

      5. *-commutative 52.6%

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

   9. Simplified 52.6%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.16 \cdot 10^{+244} \lor \neg \left(b \cdot c \leq 4.7 \cdot 10^{+232}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -4.9e+88)
   (+ (* b c) (* -4.0 (* t a)))
   (if (<= (* b c) 4.8e+42)
     (* -4.0 (+ (* x i) (* t a)))
     (- (* 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 tmp;
	if ((b * c) <= -4.9e+88) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.8e+42) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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) :: tmp
    if ((b * c) <= (-4.9d+88)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((b * c) <= 4.8d+42) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    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 tmp;
	if ((b * c) <= -4.9e+88) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.8e+42) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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):
	tmp = 0
	if (b * c) <= -4.9e+88:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (b * c) <= 4.8e+42:
		tmp = -4.0 * ((x * i) + (t * a))
	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)
	tmp = 0.0
	if (Float64(b * c) <= -4.9e+88)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= 4.8e+42)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	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)
	tmp = 0.0;
	if ((b * c) <= -4.9e+88)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((b * c) <= 4.8e+42)
		tmp = -4.0 * ((x * i) + (t * a));
	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_] := If[LessEqual[N[(b * c), $MachinePrecision], -4.9e+88], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.8e+42], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.9000000000000002e88

   1. Initial program 76.4%

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

      1. distribute-rgt-out-- 81.6%

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

      2. associate-*r* 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l* 81.6%

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

      5. associate-*r* 81.6%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in j around 0 81.7%

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

   7. Taylor expanded in i around 0 71.9%

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

   if -4.9000000000000002e88 < (*.f64 b c) < 4.7999999999999997e42

   1. Initial program 88.1%

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

      1. distribute-rgt-out-- 89.5%

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

      2. associate-*r* 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l* 88.3%

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

      5. associate-*r* 88.3%

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in y around 0 79.3%

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

   6. Taylor expanded in j around 0 57.0%

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

   7. Taylor expanded in b around 0 55.5%

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

      1. cancel-sign-sub-inv 55.5%

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

      2. metadata-eval 55.5%

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

      3. distribute-lft-out 55.5%

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

      4. *-commutative 55.5%

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

      5. *-commutative 55.5%

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

   9. Simplified 55.5%

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

   if 4.7999999999999997e42 < (*.f64 b c)

   1. Initial program 81.8%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 70.7%

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

   6. Taylor expanded in i around inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. *-commutative 60.8%

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

   8. Simplified 60.8%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= (* b c) -6.6e+88)
   (+ (* b c) (* -4.0 (* t a)))
   (if (<= (* b c) 4.7e+147)
     (* -4.0 (+ (* x i) (* t a)))
     (- (* 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 ((b * c) <= -6.6e+88) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.7e+147) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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 ((b * c) <= (-6.6d+88)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((b * c) <= 4.7d+147) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    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 ((b * c) <= -6.6e+88) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.7e+147) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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 (b * c) <= -6.6e+88:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (b * c) <= 4.7e+147:
		tmp = -4.0 * ((x * i) + (t * a))
	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 (Float64(b * c) <= -6.6e+88)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= 4.7e+147)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	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 ((b * c) <= -6.6e+88)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((b * c) <= 4.7e+147)
		tmp = -4.0 * ((x * i) + (t * a));
	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[LessEqual[N[(b * c), $MachinePrecision], -6.6e+88], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.7e+147], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -6.6000000000000006e88

   1. Initial program 76.4%

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

      1. distribute-rgt-out-- 81.6%

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

      2. associate-*r* 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l* 81.6%

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

      5. associate-*r* 81.6%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in j around 0 81.7%

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

   7. Taylor expanded in i around 0 71.9%

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

   if -6.6000000000000006e88 < (*.f64 b c) < 4.7000000000000003e147

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.8%

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

      2. associate-*r* 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*l* 89.3%

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

      5. associate-*r* 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in y around 0 78.1%

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

   6. Taylor expanded in j around 0 57.1%

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

   7. Taylor expanded in b around 0 53.9%

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

      1. cancel-sign-sub-inv 53.9%

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

      2. metadata-eval 53.9%

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

      3. distribute-lft-out 53.9%

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

      4. *-commutative 53.9%

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

      5. *-commutative 53.9%

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

   9. Simplified 53.9%

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

   if 4.7000000000000003e147 < (*.f64 b c)

   1. Initial program 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 72.5%

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

   6. Taylor expanded in i around 0 67.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.7 \cdot 10^{+147}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= (* b c) -5.5e+87)
   (+ (* b c) (* -4.0 (* t a)))
   (if (<= (* b c) 4.3e+144)
     (* -4.0 (+ (* x i) (* t a)))
     (+ (* 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) <= -5.5e+87) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.3e+144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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 ((b * c) <= (-5.5d+87)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((b * c) <= 4.3d+144) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    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 ((b * c) <= -5.5e+87) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((b * c) <= 4.3e+144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} 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 (b * c) <= -5.5e+87:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (b * c) <= 4.3e+144:
		tmp = -4.0 * ((x * i) + (t * a))
	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 (Float64(b * c) <= -5.5e+87)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= 4.3e+144)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	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 ((b * c) <= -5.5e+87)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((b * c) <= 4.3e+144)
		tmp = -4.0 * ((x * i) + (t * a));
	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[LessEqual[N[(b * c), $MachinePrecision], -5.5e+87], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.3e+144], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.50000000000000022e87

   1. Initial program 76.4%

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

      1. distribute-rgt-out-- 81.6%

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

      2. associate-*r* 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l* 81.6%

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

      5. associate-*r* 81.6%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in j around 0 81.7%

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

   7. Taylor expanded in i around 0 71.9%

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

   if -5.50000000000000022e87 < (*.f64 b c) < 4.29999999999999984e144

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.8%

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

      2. associate-*r* 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*l* 89.3%

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

      5. associate-*r* 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in y around 0 78.1%

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

   6. Taylor expanded in j around 0 57.1%

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

   7. Taylor expanded in b around 0 53.9%

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

      1. cancel-sign-sub-inv 53.9%

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

      2. metadata-eval 53.9%

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

      3. distribute-lft-out 53.9%

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

      4. *-commutative 53.9%

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

      5. *-commutative 53.9%

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

   9. Simplified 53.9%

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

   if 4.29999999999999984e144 < (*.f64 b c)

   1. Initial program 80.5%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in b around inf 67.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 34.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+70} \lor \neg \left(b \cdot c \leq 2.5 \cdot 10^{+152}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* b c) -2.3e+70) (not (<= (* b c) 2.5e+152)))
   (* b c)
   (* -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 (((b * c) <= -2.3e+70) || !((b * c) <= 2.5e+152)) {
		tmp = b * c;
	} else {
		tmp = -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 (((b * c) <= (-2.3d+70)) .or. (.not. ((b * c) <= 2.5d+152))) then
        tmp = b * c
    else
        tmp = (-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 (((b * c) <= -2.3e+70) || !((b * c) <= 2.5e+152)) {
		tmp = b * c;
	} else {
		tmp = -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 ((b * c) <= -2.3e+70) or not ((b * c) <= 2.5e+152):
		tmp = b * c
	else:
		tmp = -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 ((Float64(b * c) <= -2.3e+70) || !(Float64(b * c) <= 2.5e+152))
		tmp = Float64(b * c);
	else
		tmp = 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 (((b * c) <= -2.3e+70) || ~(((b * c) <= 2.5e+152)))
		tmp = b * c;
	else
		tmp = -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[N[(b * c), $MachinePrecision], -2.3e+70], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.5e+152]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.29999999999999994e70 or 2.5e152 < (*.f64 b c)

   1. Initial program 78.3%

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

      1. distribute-rgt-out-- 81.3%

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

      2. associate-*r* 80.3%

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

      3. *-commutative 80.3%

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

      4. associate-*l* 80.3%

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

      5. associate-*r* 80.3%

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

   4. Applied egg-rr 80.3%

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

   5. Taylor expanded in b around inf 56.4%

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

   if -2.29999999999999994e70 < (*.f64 b c) < 2.5e152

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.7%

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

      2. associate-*r* 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*l* 89.2%

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

      5. associate-*r* 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in i around inf 33.2%

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

      1. *-commutative 33.2%

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

   7. Simplified 33.2%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+70} \lor \neg \left(b \cdot c \leq 2.5 \cdot 10^{+152}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+102} \lor \neg \left(b \cdot c \leq 1.12 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

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) -3.2e+102) (not (<= (* b c) 1.12e+21)))
   (* 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) <= -3.2e+102) || !((b * c) <= 1.12e+21)) {
		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) <= (-3.2d+102)) .or. (.not. ((b * c) <= 1.12d+21))) 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) <= -3.2e+102) || !((b * c) <= 1.12e+21)) {
		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) <= -3.2e+102) or not ((b * c) <= 1.12e+21):
		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) <= -3.2e+102) || !(Float64(b * c) <= 1.12e+21))
		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) <= -3.2e+102) || ~(((b * c) <= 1.12e+21)))
		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], -3.2e+102], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.12e+21]], $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) < -3.1999999999999999e102 or 1.12e21 < (*.f64 b c)

   1. Initial program 80.1%

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

      1. distribute-rgt-out-- 83.6%

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

      2. associate-*r* 83.6%

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

      3. *-commutative 83.6%

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

      4. associate-*l* 83.6%

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

      5. associate-*r* 83.6%

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

   4. Applied egg-rr 83.6%

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

   5. Taylor expanded in b around inf 52.1%

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

   if -3.1999999999999999e102 < (*.f64 b c) < 1.12e21

   1. Initial program 87.3%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in j around inf 29.2%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+102} \lor \neg \left(b \cdot c \leq 1.12 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.7% 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 84.1%

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

   1. distribute-rgt-out-- 86.4%

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

   2. associate-*r* 85.8%

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

   3. *-commutative 85.8%

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

   4. associate-*l* 85.8%

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

   5. associate-*r* 85.8%

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

4. Applied egg-rr 85.8%

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

5. Taylor expanded in b around inf 25.2%

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

Developer Target 1: 89.3% 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 2024144 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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