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

Percentage Accurate: 85.7% → 87.1%

Time: 29.9s

Alternatives: 23

Speedup: 0.9×

• 51.1% 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: 85.7% 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: 87.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq 10^{+218}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\\ \end{array} \end{array} \]

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+218)
   (-
    (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* b c))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (fma -27.0 (* j k) (fma -4.0 (* x i) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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+218) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = fma(-27.0, (j * k), fma(-4.0, (x * i), (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(k * Float64(j * 27.0)) <= 1e+218)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = fma(-27.0, Float64(j * k), fma(-4.0, Float64(x * i), Float64(b * c)));
	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[N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision], 1e+218], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < 1.00000000000000008e218

   1. Initial program 88.2%

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

   3. Simplified 91.8%

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

   if 1.00000000000000008e218 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.8%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in t around 0 92.2%

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

      1. fma-def 96.1%

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

      2. fma-def 96.1%

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

      3. *-commutative 96.1%

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

   6. Simplified 96.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq 10^{+218}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\\ \end{array} \]

Alternative 2: 88.5% accurate, 0.1× speedup

Math

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

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

C

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

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(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)))
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[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.5%

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

3. Simplified 91.5%

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

4. Final simplification 91.5%

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

Alternative 3: 92.4% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* 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 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (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[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.4%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) 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 38.5%

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

   4. Taylor expanded in x around inf 50.2%

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

4. Final simplification 92.6%

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

Alternative 4: 36.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(-4 \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 620000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+91}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* x (* -4.0 i))))
   (if (<= (* b c) -1.9e+149)
     (* b c)
     (if (<= (* b c) -1.28e+70)
       t_1
       (if (<= (* b c) -1.5e+62)
         (* b c)
         (if (<= (* b c) -3.6e-118)
           (* t (* a -4.0))
           (if (<= (* b c) -2e-273)
             t_1
             (if (<= (* b c) 5e-324)
               t_2
               (if (<= (* b c) 1.05e-135)
                 t_1
                 (if (<= (* b c) 620000000000.0)
                   t_2
                   (if (<= (* b c) 8e+91)
                     (* 18.0 (* t (* x (* y z))))
                     (* b c))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -1.9e+149) {
		tmp = b * c;
	} else if ((b * c) <= -1.28e+70) {
		tmp = t_1;
	} else if ((b * c) <= -1.5e+62) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-118) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -2e-273) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1.05e-135) {
		tmp = t_1;
	} else if ((b * c) <= 620000000000.0) {
		tmp = t_2;
	} else if ((b * c) <= 8e+91) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (-27.0d0) * (j * k)
    t_2 = x * ((-4.0d0) * i)
    if ((b * c) <= (-1.9d+149)) then
        tmp = b * c
    else if ((b * c) <= (-1.28d+70)) then
        tmp = t_1
    else if ((b * c) <= (-1.5d+62)) then
        tmp = b * c
    else if ((b * c) <= (-3.6d-118)) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= (-2d-273)) then
        tmp = t_1
    else if ((b * c) <= 5d-324) then
        tmp = t_2
    else if ((b * c) <= 1.05d-135) then
        tmp = t_1
    else if ((b * c) <= 620000000000.0d0) then
        tmp = t_2
    else if ((b * c) <= 8d+91) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -1.9e+149) {
		tmp = b * c;
	} else if ((b * c) <= -1.28e+70) {
		tmp = t_1;
	} else if ((b * c) <= -1.5e+62) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-118) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -2e-273) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1.05e-135) {
		tmp = t_1;
	} else if ((b * c) <= 620000000000.0) {
		tmp = t_2;
	} else if ((b * c) <= 8e+91) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = x * (-4.0 * i)
	tmp = 0
	if (b * c) <= -1.9e+149:
		tmp = b * c
	elif (b * c) <= -1.28e+70:
		tmp = t_1
	elif (b * c) <= -1.5e+62:
		tmp = b * c
	elif (b * c) <= -3.6e-118:
		tmp = t * (a * -4.0)
	elif (b * c) <= -2e-273:
		tmp = t_1
	elif (b * c) <= 5e-324:
		tmp = t_2
	elif (b * c) <= 1.05e-135:
		tmp = t_1
	elif (b * c) <= 620000000000.0:
		tmp = t_2
	elif (b * c) <= 8e+91:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(x * Float64(-4.0 * i))
	tmp = 0.0
	if (Float64(b * c) <= -1.9e+149)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.28e+70)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.5e+62)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.6e-118)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= -2e-273)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-324)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.05e-135)
		tmp = t_1;
	elseif (Float64(b * c) <= 620000000000.0)
		tmp = t_2;
	elseif (Float64(b * c) <= 8e+91)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = x * (-4.0 * i);
	tmp = 0.0;
	if ((b * c) <= -1.9e+149)
		tmp = b * c;
	elseif ((b * c) <= -1.28e+70)
		tmp = t_1;
	elseif ((b * c) <= -1.5e+62)
		tmp = b * c;
	elseif ((b * c) <= -3.6e-118)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= -2e-273)
		tmp = t_1;
	elseif ((b * c) <= 5e-324)
		tmp = t_2;
	elseif ((b * c) <= 1.05e-135)
		tmp = t_1;
	elseif ((b * c) <= 620000000000.0)
		tmp = t_2;
	elseif ((b * c) <= 8e+91)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.9e+149], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.28e+70], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+62], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-118], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-273], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-324], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-135], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 620000000000.0], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 8e+91], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.9e149 or -1.27999999999999994e70 < (*.f64 b c) < -1.5e62 or 8.00000000000000064e91 < (*.f64 b c)

   1. Initial program 83.1%

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

   3. Simplified 85.6%

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

      1. associate-*r* 86.7%

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

      2. distribute-rgt-out-- 83.1%

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

      3. cancel-sign-sub-inv 83.1%

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

      4. associate-*l* 80.7%

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

      5. fma-def 81.9%

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

      6. associate-*l* 81.9%

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

   5. Applied egg-rr 81.9%

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

   6. Taylor expanded in b around inf 66.4%

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

   if -1.9e149 < (*.f64 b c) < -1.27999999999999994e70 or -3.6000000000000002e-118 < (*.f64 b c) < -2e-273 or 4.94066e-324 < (*.f64 b c) < 1.05e-135

   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 91.9%

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

   4. Taylor expanded in j around inf 47.1%

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

   if -1.5e62 < (*.f64 b c) < -3.6000000000000002e-118

   1. Initial program 80.8%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 84.6%

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

      2. distribute-rgt-out-- 80.7%

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

      3. cancel-sign-sub-inv 80.7%

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

      4. associate-*l* 76.9%

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

      5. fma-def 80.7%

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

      6. associate-*l* 80.7%

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

   5. Applied egg-rr 80.7%

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

      1. fma-udef 76.9%

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

      2. *-commutative 76.9%

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

      3. distribute-rgt-neg-in 76.9%

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

      4. metadata-eval 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. +-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

      4. associate-*r* 80.7%

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

      5. distribute-rgt-out 84.6%

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

   9. Simplified 84.6%

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

   10. Taylor expanded in a around inf 43.7%

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

       1. associate-*r* 43.7%

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

       2. *-commutative 43.7%

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

   12. Simplified 43.7%

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

   if -2e-273 < (*.f64 b c) < 4.94066e-324 or 1.05e-135 < (*.f64 b c) < 6.2e11

   1. Initial program 93.1%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 51.4%

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

   5. Taylor expanded in t around 0 43.3%

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

   if 6.2e11 < (*.f64 b c) < 8.00000000000000064e91

   1. Initial program 92.3%

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

   3. Simplified 92.8%

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

      1. associate-*r* 100.0%

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

      2. distribute-rgt-out-- 92.3%

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

      3. cancel-sign-sub-inv 92.3%

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

      4. associate-*l* 85.2%

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

      5. fma-def 85.2%

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

      6. associate-*l* 85.2%

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

   5. Applied egg-rr 85.2%

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

      1. fma-udef 85.2%

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

      2. *-commutative 85.2%

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

      3. distribute-rgt-neg-in 85.2%

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

      4. metadata-eval 85.2%

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

   7. Applied egg-rr 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-*r* 92.3%

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

      5. distribute-rgt-out 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around inf 63.1%

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

       1. *-commutative 63.1%

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

   12. Simplified 63.1%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-273}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 620000000000:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+91}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 5: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(-4 \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+160}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.56 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 0.000195:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* x (* -4.0 i))))
   (if (<= (* b c) -1.1e+160)
     (* b c)
     (if (<= (* b c) -1.9e+70)
       t_1
       (if (<= (* b c) -1.56e+62)
         (* b c)
         (if (<= (* b c) -8e-119)
           (* t (* a -4.0))
           (if (<= (* b c) -1.35e-280)
             t_1
             (if (<= (* b c) 5e-324)
               t_2
               (if (<= (* b c) 1e-135)
                 t_1
                 (if (<= (* b c) 0.000195)
                   t_2
                   (if (<= (* b c) 5e+96)
                     (* (* y (* x z)) (* t 18.0))
                     (* 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 t_1 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -1.1e+160) {
		tmp = b * c;
	} else if ((b * c) <= -1.9e+70) {
		tmp = t_1;
	} else if ((b * c) <= -1.56e+62) {
		tmp = b * c;
	} else if ((b * c) <= -8e-119) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -1.35e-280) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1e-135) {
		tmp = t_1;
	} else if ((b * c) <= 0.000195) {
		tmp = t_2;
	} else if ((b * c) <= 5e+96) {
		tmp = (y * (x * z)) * (t * 18.0);
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = x * ((-4.0d0) * i)
    if ((b * c) <= (-1.1d+160)) then
        tmp = b * c
    else if ((b * c) <= (-1.9d+70)) then
        tmp = t_1
    else if ((b * c) <= (-1.56d+62)) then
        tmp = b * c
    else if ((b * c) <= (-8d-119)) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= (-1.35d-280)) then
        tmp = t_1
    else if ((b * c) <= 5d-324) then
        tmp = t_2
    else if ((b * c) <= 1d-135) then
        tmp = t_1
    else if ((b * c) <= 0.000195d0) then
        tmp = t_2
    else if ((b * c) <= 5d+96) then
        tmp = (y * (x * z)) * (t * 18.0d0)
    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 t_1 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -1.1e+160) {
		tmp = b * c;
	} else if ((b * c) <= -1.9e+70) {
		tmp = t_1;
	} else if ((b * c) <= -1.56e+62) {
		tmp = b * c;
	} else if ((b * c) <= -8e-119) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -1.35e-280) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1e-135) {
		tmp = t_1;
	} else if ((b * c) <= 0.000195) {
		tmp = t_2;
	} else if ((b * c) <= 5e+96) {
		tmp = (y * (x * z)) * (t * 18.0);
	} 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):
	t_1 = -27.0 * (j * k)
	t_2 = x * (-4.0 * i)
	tmp = 0
	if (b * c) <= -1.1e+160:
		tmp = b * c
	elif (b * c) <= -1.9e+70:
		tmp = t_1
	elif (b * c) <= -1.56e+62:
		tmp = b * c
	elif (b * c) <= -8e-119:
		tmp = t * (a * -4.0)
	elif (b * c) <= -1.35e-280:
		tmp = t_1
	elif (b * c) <= 5e-324:
		tmp = t_2
	elif (b * c) <= 1e-135:
		tmp = t_1
	elif (b * c) <= 0.000195:
		tmp = t_2
	elif (b * c) <= 5e+96:
		tmp = (y * (x * z)) * (t * 18.0)
	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)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(x * Float64(-4.0 * i))
	tmp = 0.0
	if (Float64(b * c) <= -1.1e+160)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.9e+70)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.56e+62)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -8e-119)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= -1.35e-280)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-324)
		tmp = t_2;
	elseif (Float64(b * c) <= 1e-135)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.000195)
		tmp = t_2;
	elseif (Float64(b * c) <= 5e+96)
		tmp = Float64(Float64(y * Float64(x * z)) * Float64(t * 18.0));
	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)
	t_1 = -27.0 * (j * k);
	t_2 = x * (-4.0 * i);
	tmp = 0.0;
	if ((b * c) <= -1.1e+160)
		tmp = b * c;
	elseif ((b * c) <= -1.9e+70)
		tmp = t_1;
	elseif ((b * c) <= -1.56e+62)
		tmp = b * c;
	elseif ((b * c) <= -8e-119)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= -1.35e-280)
		tmp = t_1;
	elseif ((b * c) <= 5e-324)
		tmp = t_2;
	elseif ((b * c) <= 1e-135)
		tmp = t_1;
	elseif ((b * c) <= 0.000195)
		tmp = t_2;
	elseif ((b * c) <= 5e+96)
		tmp = (y * (x * z)) * (t * 18.0);
	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_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.1e+160], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.9e+70], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.56e+62], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8e-119], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.35e-280], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-324], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1e-135], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.000195], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5e+96], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.09999999999999996e160 or -1.8999999999999999e70 < (*.f64 b c) < -1.55999999999999995e62 or 5.0000000000000004e96 < (*.f64 b c)

   1. Initial program 83.1%

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

   3. Simplified 85.6%

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

      1. associate-*r* 86.7%

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

      2. distribute-rgt-out-- 83.1%

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

      3. cancel-sign-sub-inv 83.1%

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

      4. associate-*l* 80.7%

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

      5. fma-def 81.9%

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

      6. associate-*l* 81.9%

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

   5. Applied egg-rr 81.9%

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

   6. Taylor expanded in b around inf 66.4%

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

   if -1.09999999999999996e160 < (*.f64 b c) < -1.8999999999999999e70 or -8.0000000000000001e-119 < (*.f64 b c) < -1.34999999999999992e-280 or 4.94066e-324 < (*.f64 b c) < 1e-135

   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 91.9%

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

   4. Taylor expanded in j around inf 47.1%

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

   if -1.55999999999999995e62 < (*.f64 b c) < -8.0000000000000001e-119

   1. Initial program 80.8%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 84.6%

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

      2. distribute-rgt-out-- 80.7%

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

      3. cancel-sign-sub-inv 80.7%

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

      4. associate-*l* 76.9%

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

      5. fma-def 80.7%

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

      6. associate-*l* 80.7%

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

   5. Applied egg-rr 80.7%

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

      1. fma-udef 76.9%

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

      2. *-commutative 76.9%

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

      3. distribute-rgt-neg-in 76.9%

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

      4. metadata-eval 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. +-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

      4. associate-*r* 80.7%

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

      5. distribute-rgt-out 84.6%

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

   9. Simplified 84.6%

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

   10. Taylor expanded in a around inf 43.7%

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

       1. associate-*r* 43.7%

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

       2. *-commutative 43.7%

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

   12. Simplified 43.7%

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

   if -1.34999999999999992e-280 < (*.f64 b c) < 4.94066e-324 or 1e-135 < (*.f64 b c) < 1.94999999999999996e-4

   1. Initial program 92.6%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 52.9%

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

   5. Taylor expanded in t around 0 45.4%

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

   if 1.94999999999999996e-4 < (*.f64 b c) < 5.0000000000000004e96

   1. Initial program 94.6%

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

   3. Simplified 90.0%

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

      1. associate-*r* 99.8%

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

      2. distribute-rgt-out-- 94.6%

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

      3. cancel-sign-sub-inv 94.6%

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

      4. associate-*l* 89.7%

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

      5. fma-def 89.7%

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

      6. associate-*l* 89.7%

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

   5. Applied egg-rr 89.7%

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

      1. fma-udef 89.7%

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

      2. *-commutative 89.7%

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

      3. distribute-rgt-neg-in 89.7%

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

      4. metadata-eval 89.7%

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

   7. Applied egg-rr 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r* 94.7%

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

      5. distribute-rgt-out 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in y around inf 49.1%

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

       1. *-commutative 49.1%

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

   12. Simplified 49.1%

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

   13. Taylor expanded in x around 0 49.1%

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

       1. associate-*r* 49.0%

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

       2. *-commutative 49.0%

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

       3. *-commutative 49.0%

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

       4. *-commutative 49.0%

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

       5. associate-*l* 53.8%

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

   15. Simplified 53.8%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+160}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.56 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-280}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-135}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 0.000195:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 6: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;t_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 265000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;t_1 + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* x i)))))
   (if (<= (* b c) -1.55e+62)
     (+ t_1 (* b c))
     (if (<= (* b c) -4.2e-307)
       (+ t_1 (* t (* a -4.0)))
       (if (<= (* b c) 1.9e-250)
         t_2
         (if (<= (* b c) 4.8e-182)
           (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
           (if (<= (* b c) 265000000000.0)
             t_2
             (if (<= (* b c) 1.4e+93)
               (+ t_1 (* 18.0 (* x (* y (* t z)))))
               (- (* 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -1.55e+62) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -4.2e-307) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 1.9e-250) {
		tmp = t_2;
	} else if ((b * c) <= 4.8e-182) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 265000000000.0) {
		tmp = t_2;
	} else if ((b * c) <= 1.4e+93) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (x * i))
    if ((b * c) <= (-1.55d+62)) then
        tmp = t_1 + (b * c)
    else if ((b * c) <= (-4.2d-307)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if ((b * c) <= 1.9d-250) then
        tmp = t_2
    else if ((b * c) <= 4.8d-182) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if ((b * c) <= 265000000000.0d0) then
        tmp = t_2
    else if ((b * c) <= 1.4d+93) then
        tmp = t_1 + (18.0d0 * (x * (y * (t * z))))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -1.55e+62) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -4.2e-307) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 1.9e-250) {
		tmp = t_2;
	} else if ((b * c) <= 4.8e-182) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 265000000000.0) {
		tmp = t_2;
	} else if ((b * c) <= 1.4e+93) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (x * i))
	tmp = 0
	if (b * c) <= -1.55e+62:
		tmp = t_1 + (b * c)
	elif (b * c) <= -4.2e-307:
		tmp = t_1 + (t * (a * -4.0))
	elif (b * c) <= 1.9e-250:
		tmp = t_2
	elif (b * c) <= 4.8e-182:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif (b * c) <= 265000000000.0:
		tmp = t_2
	elif (b * c) <= 1.4e+93:
		tmp = t_1 + (18.0 * (x * (y * (t * z))))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -1.55e+62)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (Float64(b * c) <= -4.2e-307)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= 1.9e-250)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.8e-182)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (Float64(b * c) <= 265000000000.0)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.4e+93)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(y * Float64(t * z)))));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (x * i));
	tmp = 0.0;
	if ((b * c) <= -1.55e+62)
		tmp = t_1 + (b * c);
	elseif ((b * c) <= -4.2e-307)
		tmp = t_1 + (t * (a * -4.0));
	elseif ((b * c) <= 1.9e-250)
		tmp = t_2;
	elseif ((b * c) <= 4.8e-182)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif ((b * c) <= 265000000000.0)
		tmp = t_2;
	elseif ((b * c) <= 1.4e+93)
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.55e+62], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.2e-307], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.9e-250], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.8e-182], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 265000000000.0], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.4e+93], N[(t$95$1 + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.55000000000000007e62

   1. Initial program 79.5%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -1.55000000000000007e62 < (*.f64 b c) < -4.2000000000000002e-307

   1. Initial program 83.7%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 63.2%

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

      4. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -4.2000000000000002e-307 < (*.f64 b c) < 1.89999999999999985e-250 or 4.7999999999999997e-182 < (*.f64 b c) < 2.65e11

   1. Initial program 94.1%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in i around inf 63.3%

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

      1. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if 1.89999999999999985e-250 < (*.f64 b c) < 4.7999999999999997e-182

   1. Initial program 77.3%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 91.2%

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

   if 2.65e11 < (*.f64 b c) < 1.39999999999999994e93

   1. Initial program 92.3%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l* 70.9%

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

      3. associate-*l* 78.1%

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

   6. Simplified 78.1%

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

   if 1.39999999999999994e93 < (*.f64 b c)

   1. Initial program 88.0%

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

   2. Taylor expanded in t around 0 84.6%

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

   3. Taylor expanded in j around 0 77.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 265000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 7: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(x \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \cdot c \leq -9.4 \cdot 10^{+61}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-302}:\\ \;\;\;\;t_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(18 \cdot t_3 - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.8 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot t_3\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* -4.0 (* x i))))
        (t_3 (* x (* y z))))
   (if (<= (* b c) -9.4e+61)
     (+ t_1 (* b c))
     (if (<= (* b c) -1.95e-302)
       (+ t_1 (* t (* a -4.0)))
       (if (<= (* b c) 3.9e-250)
         t_2
         (if (<= (* b c) 1.8e-182)
           (* t (- (* 18.0 t_3) (* a 4.0)))
           (if (<= (* b c) 7.8e+16)
             t_2
             (if (<= (* b c) 1.6e+94)
               (+ t_1 (* 18.0 (* t t_3)))
               (- (* 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double t_3 = x * (y * z);
	double tmp;
	if ((b * c) <= -9.4e+61) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -1.95e-302) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 3.9e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.8e-182) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if ((b * c) <= 7.8e+16) {
		tmp = t_2;
	} else if ((b * c) <= 1.6e+94) {
		tmp = t_1 + (18.0 * (t * t_3));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (x * i))
    t_3 = x * (y * z)
    if ((b * c) <= (-9.4d+61)) then
        tmp = t_1 + (b * c)
    else if ((b * c) <= (-1.95d-302)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if ((b * c) <= 3.9d-250) then
        tmp = t_2
    else if ((b * c) <= 1.8d-182) then
        tmp = t * ((18.0d0 * t_3) - (a * 4.0d0))
    else if ((b * c) <= 7.8d+16) then
        tmp = t_2
    else if ((b * c) <= 1.6d+94) then
        tmp = t_1 + (18.0d0 * (t * t_3))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double t_3 = x * (y * z);
	double tmp;
	if ((b * c) <= -9.4e+61) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -1.95e-302) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 3.9e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.8e-182) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if ((b * c) <= 7.8e+16) {
		tmp = t_2;
	} else if ((b * c) <= 1.6e+94) {
		tmp = t_1 + (18.0 * (t * t_3));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (x * i))
	t_3 = x * (y * z)
	tmp = 0
	if (b * c) <= -9.4e+61:
		tmp = t_1 + (b * c)
	elif (b * c) <= -1.95e-302:
		tmp = t_1 + (t * (a * -4.0))
	elif (b * c) <= 3.9e-250:
		tmp = t_2
	elif (b * c) <= 1.8e-182:
		tmp = t * ((18.0 * t_3) - (a * 4.0))
	elif (b * c) <= 7.8e+16:
		tmp = t_2
	elif (b * c) <= 1.6e+94:
		tmp = t_1 + (18.0 * (t * t_3))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(x * i)))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(b * c) <= -9.4e+61)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (Float64(b * c) <= -1.95e-302)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= 3.9e-250)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.8e-182)
		tmp = Float64(t * Float64(Float64(18.0 * t_3) - Float64(a * 4.0)));
	elseif (Float64(b * c) <= 7.8e+16)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.6e+94)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * t_3)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (x * i));
	t_3 = x * (y * z);
	tmp = 0.0;
	if ((b * c) <= -9.4e+61)
		tmp = t_1 + (b * c);
	elseif ((b * c) <= -1.95e-302)
		tmp = t_1 + (t * (a * -4.0));
	elseif ((b * c) <= 3.9e-250)
		tmp = t_2;
	elseif ((b * c) <= 1.8e-182)
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	elseif ((b * c) <= 7.8e+16)
		tmp = t_2;
	elseif ((b * c) <= 1.6e+94)
		tmp = t_1 + (18.0 * (t * t_3));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9.4e+61], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.95e-302], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.9e-250], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.8e-182], N[(t * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.8e+16], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+94], N[(t$95$1 + N[(18.0 * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -9.3999999999999997e61

   1. Initial program 79.5%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -9.3999999999999997e61 < (*.f64 b c) < -1.95e-302

   1. Initial program 83.7%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 63.2%

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

      4. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -1.95e-302 < (*.f64 b c) < 3.90000000000000027e-250 or 1.79999999999999988e-182 < (*.f64 b c) < 7.8e16

   1. Initial program 94.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in i around inf 63.1%

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

      1. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   if 3.90000000000000027e-250 < (*.f64 b c) < 1.79999999999999988e-182

   1. Initial program 77.3%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 91.2%

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

   if 7.8e16 < (*.f64 b c) < 1.60000000000000007e94

   1. Initial program 90.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.6%

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

      1. *-commutative 82.6%

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

   6. Simplified 82.6%

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

   if 1.60000000000000007e94 < (*.f64 b c)

   1. Initial program 88.0%

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

   2. Taylor expanded in t around 0 84.6%

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

   3. Taylor expanded in j around 0 77.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.4 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-302}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-182}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.8 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 8: 35.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(-4 \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.6 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.12 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* x (* -4.0 i))))
   (if (<= (* b c) -7.2e+153)
     (* b c)
     (if (<= (* b c) -3e+69)
       t_1
       (if (<= (* b c) -6.8e+61)
         (* b c)
         (if (<= (* b c) -3.6e-118)
           (* t (* a -4.0))
           (if (<= (* b c) -5.6e-282)
             t_1
             (if (<= (* b c) 5e-324)
               t_2
               (if (<= (* b c) 1.12e-135)
                 t_1
                 (if (<= (* b c) 6.2e+146) t_2 (* b c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -7.2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -3e+69) {
		tmp = t_1;
	} else if ((b * c) <= -6.8e+61) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-118) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -5.6e-282) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1.12e-135) {
		tmp = t_1;
	} else if ((b * c) <= 6.2e+146) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = x * ((-4.0d0) * i)
    if ((b * c) <= (-7.2d+153)) then
        tmp = b * c
    else if ((b * c) <= (-3d+69)) then
        tmp = t_1
    else if ((b * c) <= (-6.8d+61)) then
        tmp = b * c
    else if ((b * c) <= (-3.6d-118)) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= (-5.6d-282)) then
        tmp = t_1
    else if ((b * c) <= 5d-324) then
        tmp = t_2
    else if ((b * c) <= 1.12d-135) then
        tmp = t_1
    else if ((b * c) <= 6.2d+146) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = x * (-4.0 * i);
	double tmp;
	if ((b * c) <= -7.2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -3e+69) {
		tmp = t_1;
	} else if ((b * c) <= -6.8e+61) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-118) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -5.6e-282) {
		tmp = t_1;
	} else if ((b * c) <= 5e-324) {
		tmp = t_2;
	} else if ((b * c) <= 1.12e-135) {
		tmp = t_1;
	} else if ((b * c) <= 6.2e+146) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = x * (-4.0 * i)
	tmp = 0
	if (b * c) <= -7.2e+153:
		tmp = b * c
	elif (b * c) <= -3e+69:
		tmp = t_1
	elif (b * c) <= -6.8e+61:
		tmp = b * c
	elif (b * c) <= -3.6e-118:
		tmp = t * (a * -4.0)
	elif (b * c) <= -5.6e-282:
		tmp = t_1
	elif (b * c) <= 5e-324:
		tmp = t_2
	elif (b * c) <= 1.12e-135:
		tmp = t_1
	elif (b * c) <= 6.2e+146:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(x * Float64(-4.0 * i))
	tmp = 0.0
	if (Float64(b * c) <= -7.2e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3e+69)
		tmp = t_1;
	elseif (Float64(b * c) <= -6.8e+61)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.6e-118)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= -5.6e-282)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-324)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.12e-135)
		tmp = t_1;
	elseif (Float64(b * c) <= 6.2e+146)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = x * (-4.0 * i);
	tmp = 0.0;
	if ((b * c) <= -7.2e+153)
		tmp = b * c;
	elseif ((b * c) <= -3e+69)
		tmp = t_1;
	elseif ((b * c) <= -6.8e+61)
		tmp = b * c;
	elseif ((b * c) <= -3.6e-118)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= -5.6e-282)
		tmp = t_1;
	elseif ((b * c) <= 5e-324)
		tmp = t_2;
	elseif ((b * c) <= 1.12e-135)
		tmp = t_1;
	elseif ((b * c) <= 6.2e+146)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3e+69], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -6.8e+61], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-118], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.6e-282], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-324], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.12e-135], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 6.2e+146], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -7.2000000000000001e153 or -2.99999999999999983e69 < (*.f64 b c) < -6.80000000000000051e61 or 6.2000000000000004e146 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Simplified 85.6%

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

      1. associate-*r* 86.8%

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

      2. distribute-rgt-out-- 82.9%

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

      3. cancel-sign-sub-inv 82.9%

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

      4. associate-*l* 80.2%

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

      5. fma-def 81.6%

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

      6. associate-*l* 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in b around inf 69.9%

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

   if -7.2000000000000001e153 < (*.f64 b c) < -2.99999999999999983e69 or -3.6000000000000002e-118 < (*.f64 b c) < -5.5999999999999998e-282 or 4.94066e-324 < (*.f64 b c) < 1.12e-135

   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 91.9%

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

   4. Taylor expanded in j around inf 47.1%

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

   if -6.80000000000000051e61 < (*.f64 b c) < -3.6000000000000002e-118

   1. Initial program 80.8%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 84.6%

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

      2. distribute-rgt-out-- 80.7%

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

      3. cancel-sign-sub-inv 80.7%

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

      4. associate-*l* 76.9%

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

      5. fma-def 80.7%

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

      6. associate-*l* 80.7%

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

   5. Applied egg-rr 80.7%

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

      1. fma-udef 76.9%

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

      2. *-commutative 76.9%

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

      3. distribute-rgt-neg-in 76.9%

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

      4. metadata-eval 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. +-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

      4. associate-*r* 80.7%

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

      5. distribute-rgt-out 84.6%

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

   9. Simplified 84.6%

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

   10. Taylor expanded in a around inf 43.7%

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

       1. associate-*r* 43.7%

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

       2. *-commutative 43.7%

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

   12. Simplified 43.7%

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

   if -5.5999999999999998e-282 < (*.f64 b c) < 4.94066e-324 or 1.12e-135 < (*.f64 b c) < 6.2000000000000004e146

   1. Initial program 92.5%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 53.6%

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

   5. Taylor expanded in t around 0 39.8%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{+69}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.6 \cdot 10^{-282}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-324}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.12 \cdot 10^{-135}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 9: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 7.5 \cdot 10^{+227}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + z \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \end{array} \]

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) 7.5e+227)
   (-
    (+ (* b c) (* t (+ (* a -4.0) (* z (* x (* 18.0 y))))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (+ (* 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) <= 7.5e+227) {
		tmp = ((b * c) + (t * ((a * -4.0) + (z * (x * (18.0 * y)))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (j * (k * -27.0)) + (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) <= 7.5d+227) then
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (z * (x * (18.0d0 * y)))))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = (j * (k * (-27.0d0))) + (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) <= 7.5e+227) {
		tmp = ((b * c) + (t * ((a * -4.0) + (z * (x * (18.0 * y)))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (j * (k * -27.0)) + (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) <= 7.5e+227:
		tmp = ((b * c) + (t * ((a * -4.0) + (z * (x * (18.0 * y)))))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = (j * (k * -27.0)) + (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) <= 7.5e+227)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(z * Float64(x * Float64(18.0 * y)))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + 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) <= 7.5e+227)
		tmp = ((b * c) + (t * ((a * -4.0) + (z * (x * (18.0 * y)))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = (j * (k * -27.0)) + (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], 7.5e+227], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 7.5000000000000003e227

   1. Initial program 88.2%

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

   3. Simplified 91.3%

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

      1. associate-*r* 91.7%

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

      2. distribute-rgt-out-- 87.8%

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

      3. cancel-sign-sub-inv 87.8%

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

      4. associate-*l* 85.2%

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

      5. fma-def 86.5%

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

      6. associate-*l* 86.5%

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

   5. Applied egg-rr 86.5%

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

      1. fma-udef 85.2%

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

      2. *-commutative 85.2%

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

      3. distribute-rgt-neg-in 85.2%

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

      4. metadata-eval 85.2%

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

   7. Applied egg-rr 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-*r* 87.8%

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

      5. distribute-rgt-out 91.7%

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

   9. Simplified 91.7%

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

   if 7.5000000000000003e227 < (*.f64 b c)

   1. Initial program 81.5%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in b around inf 92.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 7.5 \cdot 10^{+227}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + z \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]

Alternative 10: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 2.16 \cdot 10^{+276}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) 2.16e+276)
   (-
    (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* b c))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= 2.16e+276) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) <= 2.16d+276) then
        tmp = ((t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))) + (b * c)) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) <= 2.16e+276) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= 2.16e+276:
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= 2.16e+276)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= 2.16e+276)
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (b * c)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 2.16e+276], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 2.16000000000000012e276

   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 91.6%

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

   if 2.16000000000000012e276 < (*.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. Taylor expanded in t around 0 95.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 2.16 \cdot 10^{+276}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 11: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-302}:\\ \;\;\;\;t_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* x i)))))
   (if (<= (* b c) -4.9e+61)
     (+ t_1 (* b c))
     (if (<= (* b c) -5.8e-302)
       (+ t_1 (* t (* a -4.0)))
       (if (<= (* b c) 2.8e-250)
         t_2
         (if (<= (* b c) 1.3e-184)
           (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
           (if (<= (* b c) 3.2e+55) t_2 (- (* 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -4.9e+61) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -5.8e-302) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 2.8e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.3e-184) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 3.2e+55) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (x * i))
    if ((b * c) <= (-4.9d+61)) then
        tmp = t_1 + (b * c)
    else if ((b * c) <= (-5.8d-302)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if ((b * c) <= 2.8d-250) then
        tmp = t_2
    else if ((b * c) <= 1.3d-184) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if ((b * c) <= 3.2d+55) then
        tmp = t_2
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -4.9e+61) {
		tmp = t_1 + (b * c);
	} else if ((b * c) <= -5.8e-302) {
		tmp = t_1 + (t * (a * -4.0));
	} else if ((b * c) <= 2.8e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.3e-184) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 3.2e+55) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (x * i))
	tmp = 0
	if (b * c) <= -4.9e+61:
		tmp = t_1 + (b * c)
	elif (b * c) <= -5.8e-302:
		tmp = t_1 + (t * (a * -4.0))
	elif (b * c) <= 2.8e-250:
		tmp = t_2
	elif (b * c) <= 1.3e-184:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif (b * c) <= 3.2e+55:
		tmp = t_2
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -4.9e+61)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (Float64(b * c) <= -5.8e-302)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= 2.8e-250)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.3e-184)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (Float64(b * c) <= 3.2e+55)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (x * i));
	tmp = 0.0;
	if ((b * c) <= -4.9e+61)
		tmp = t_1 + (b * c);
	elseif ((b * c) <= -5.8e-302)
		tmp = t_1 + (t * (a * -4.0));
	elseif ((b * c) <= 2.8e-250)
		tmp = t_2;
	elseif ((b * c) <= 1.3e-184)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif ((b * c) <= 3.2e+55)
		tmp = t_2;
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.9e+61], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.8e-302], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.8e-250], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.3e-184], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+55], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -4.90000000000000025e61

   1. Initial program 79.5%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around inf 71.5%

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

   if -4.90000000000000025e61 < (*.f64 b c) < -5.79999999999999989e-302

   1. Initial program 83.7%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 63.2%

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

      1. *-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 63.2%

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

      4. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -5.79999999999999989e-302 < (*.f64 b c) < 2.80000000000000028e-250 or 1.29999999999999989e-184 < (*.f64 b c) < 3.2000000000000003e55

   1. Initial program 94.5%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in i around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if 2.80000000000000028e-250 < (*.f64 b c) < 1.29999999999999989e-184

   1. Initial program 77.3%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 91.2%

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

   if 3.2000000000000003e55 < (*.f64 b c)

   1. Initial program 87.5%

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

   2. Taylor expanded in t around 0 80.9%

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

   3. Taylor expanded in j around 0 72.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-302}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 12: 69.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.8:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \end{array} \]

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))) (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -7.8e+102)
     t_2
     (if (<= t -1.05e+40)
       (+ (* j (* k -27.0)) (* t (* a -4.0)))
       (if (<= t -3.8)
         t_2
         (if (<= t 8.5e+74)
           (- (- (* b c) t_1) (* k (* j 27.0)))
           (- (* b c) (+ t_1 (* 4.0 (* t a))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_2;
	} else if (t <= -1.05e+40) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (t <= -3.8) {
		tmp = t_2;
	} else if (t <= 8.5e+74) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-7.8d+102)) then
        tmp = t_2
    else if (t <= (-1.05d+40)) then
        tmp = (j * (k * (-27.0d0))) + (t * (a * (-4.0d0)))
    else if (t <= (-3.8d0)) then
        tmp = t_2
    else if (t <= 8.5d+74) then
        tmp = ((b * c) - t_1) - (k * (j * 27.0d0))
    else
        tmp = (b * c) - (t_1 + (4.0d0 * (t * a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_2;
	} else if (t <= -1.05e+40) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (t <= -3.8) {
		tmp = t_2;
	} else if (t <= 8.5e+74) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -7.8e+102:
		tmp = t_2
	elif t <= -1.05e+40:
		tmp = (j * (k * -27.0)) + (t * (a * -4.0))
	elif t <= -3.8:
		tmp = t_2
	elif t <= 8.5e+74:
		tmp = ((b * c) - t_1) - (k * (j * 27.0))
	else:
		tmp = (b * c) - (t_1 + (4.0 * (t * a)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7.8e+102)
		tmp = t_2;
	elseif (t <= -1.05e+40)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(a * -4.0)));
	elseif (t <= -3.8)
		tmp = t_2;
	elseif (t <= 8.5e+74)
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(t * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7.8e+102)
		tmp = t_2;
	elseif (t <= -1.05e+40)
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	elseif (t <= -3.8)
		tmp = t_2;
	elseif (t <= 8.5e+74)
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	else
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+102], t$95$2, If[LessEqual[t, -1.05e+40], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8], t$95$2, If[LessEqual[t, 8.5e+74], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.7999999999999997e102 or -1.05000000000000005e40 < t < -3.7999999999999998

   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 89.9%

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

   4. Taylor expanded in t around inf 76.2%

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

   if -7.7999999999999997e102 < t < -1.05000000000000005e40

   1. Initial program 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in a around inf 76.8%

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

      1. *-commutative 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 76.8%

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

      4. *-commutative 76.8%

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

   6. Simplified 76.8%

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

   if -3.7999999999999998 < t < 8.50000000000000028e74

   1. Initial program 92.2%

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

   2. Taylor expanded in t around 0 81.6%

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

   if 8.50000000000000028e74 < t

   1. Initial program 82.6%

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

   2. Taylor expanded in y around 0 78.6%

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

   3. Taylor expanded in j around 0 74.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.8:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 13: 78.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.2e-8)
   (+ (* j (* k -27.0)) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))
   (- (- (* b c) (+ (* 4.0 (* x i)) (* 4.0 (* t a)))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.2e-8) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else {
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.2e-8) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else {
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.2e-8:
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	else:
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.2e-8)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a)))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.2e-8)
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	else
		tmp = ((b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.2e-8], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.19999999999999999e-8

   1. Initial program 79.6%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 81.9%

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

   if -1.19999999999999999e-8 < t

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 86.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 14: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -9 \cdot 10^{+198}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+91}:\\ \;\;\;\;t_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= j -9e+198)
     (+ t_1 (* 18.0 (* t (* x (* y z)))))
     (if (<= j -2.8e+91)
       (+ t_1 (* t (* a -4.0)))
       (if (<= j 3.4e+30)
         (- (* b c) (+ (* 4.0 (* x i)) (* 4.0 (* t a))))
         (+ t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -9e+198) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (j <= -2.8e+91) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (j <= 3.4e+30) {
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (j <= (-9d+198)) then
        tmp = t_1 + (18.0d0 * (t * (x * (y * z))))
    else if (j <= (-2.8d+91)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if (j <= 3.4d+30) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))
    else
        tmp = t_1 + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -9e+198) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (j <= -2.8e+91) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (j <= 3.4e+30) {
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if j <= -9e+198:
		tmp = t_1 + (18.0 * (t * (x * (y * z))))
	elif j <= -2.8e+91:
		tmp = t_1 + (t * (a * -4.0))
	elif j <= 3.4e+30:
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)))
	else:
		tmp = t_1 + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -9e+198)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	elseif (j <= -2.8e+91)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (j <= 3.4e+30)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -9e+198)
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	elseif (j <= -2.8e+91)
		tmp = t_1 + (t * (a * -4.0));
	elseif (j <= 3.4e+30)
		tmp = (b * c) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	else
		tmp = t_1 + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9e+198], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e+91], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+30], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.00000000000000003e198

   1. Initial program 94.9%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   if -9.00000000000000003e198 < j < -2.7999999999999999e91

   1. Initial program 89.5%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*r* 70.1%

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

      4. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -2.7999999999999999e91 < j < 3.4000000000000002e30

   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. Taylor expanded in y around 0 76.6%

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

   3. Taylor expanded in j around 0 70.2%

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

   if 3.4000000000000002e30 < j

   1. Initial program 85.5%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in b around inf 62.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{+198}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]

Alternative 15: 72.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \end{array} \]

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 (<= t -7.2e-9)
     (+ (* j (* k -27.0)) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))
     (if (<= t 1.7e+74)
       (- (- (* b c) t_1) (* k (* j 27.0)))
       (- (* b c) (+ t_1 (* 4.0 (* t a))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if (t <= -7.2e-9) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else if (t <= 1.7e+74) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    if (t <= (-7.2d-9)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))
    else if (t <= 1.7d+74) then
        tmp = ((b * c) - t_1) - (k * (j * 27.0d0))
    else
        tmp = (b * c) - (t_1 + (4.0d0 * (t * a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if (t <= -7.2e-9) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else if (t <= 1.7e+74) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	tmp = 0
	if t <= -7.2e-9:
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	elif t <= 1.7e+74:
		tmp = ((b * c) - t_1) - (k * (j * 27.0))
	else:
		tmp = (b * c) - (t_1 + (4.0 * (t * a)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -7.2e-9)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))));
	elseif (t <= 1.7e+74)
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(t * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -7.2e-9)
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	elseif (t <= 1.7e+74)
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	else
		tmp = (b * c) - (t_1 + (4.0 * (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[t, -7.2e-9], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+74], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e-9

   1. Initial program 79.6%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 81.9%

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

   if -7.2e-9 < t < 1.7e74

   1. Initial program 92.1%

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

   2. Taylor expanded in t around 0 82.0%

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

   if 1.7e74 < t

   1. Initial program 82.6%

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

   2. Taylor expanded in y around 0 78.6%

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

   3. Taylor expanded in j around 0 74.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 16: 51.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+90} \lor \neg \left(j \leq 4.7 \cdot 10^{-46}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (<= j -1.05e+192)
   (- (* b c) (* 27.0 (* j k)))
   (if (or (<= j -5.5e+90) (not (<= j 4.7e-46)))
     (+ (* j (* k -27.0)) (* -4.0 (* x i)))
     (- (* 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 (j <= -1.05e+192) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if ((j <= -5.5e+90) || !(j <= 4.7e-46)) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else {
		tmp = (b * c) - (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 (j <= (-1.05d+192)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if ((j <= (-5.5d+90)) .or. (.not. (j <= 4.7d-46))) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * i))
    else
        tmp = (b * c) - (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 (j <= -1.05e+192) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if ((j <= -5.5e+90) || !(j <= 4.7e-46)) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else {
		tmp = (b * c) - (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 j <= -1.05e+192:
		tmp = (b * c) - (27.0 * (j * k))
	elif (j <= -5.5e+90) or not (j <= 4.7e-46):
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i))
	else:
		tmp = (b * c) - (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 (j <= -1.05e+192)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif ((j <= -5.5e+90) || !(j <= 4.7e-46))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) - 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 (j <= -1.05e+192)
		tmp = (b * c) - (27.0 * (j * k));
	elseif ((j <= -5.5e+90) || ~((j <= 4.7e-46)))
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	else
		tmp = (b * c) - (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[LessEqual[j, -1.05e+192], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, -5.5e+90], N[Not[LessEqual[j, 4.7e-46]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.04999999999999997e192

   1. Initial program 95.4%

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

   2. Taylor expanded in t around 0 78.0%

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

   3. Taylor expanded in i around 0 74.5%

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

   if -1.04999999999999997e192 < j < -5.49999999999999999e90 or 4.69999999999999966e-46 < j

   1. Initial program 87.1%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in i around inf 50.0%

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

      1. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if -5.49999999999999999e90 < j < 4.69999999999999966e-46

   1. Initial program 86.5%

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

   2. Taylor expanded in t around 0 59.4%

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

   3. Taylor expanded in j around 0 52.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+90} \lor \neg \left(j \leq 4.7 \cdot 10^{-46}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 17: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+226}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;t_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-39}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= j -2.9e+226)
     (+ t_1 (* b c))
     (if (<= j -2.5e+74)
       (+ t_1 (* t (* a -4.0)))
       (if (<= j 1.85e-39)
         (- (* b c) (* 4.0 (* x i)))
         (+ t_1 (* -4.0 (* x i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -2.9e+226) {
		tmp = t_1 + (b * c);
	} else if (j <= -2.5e+74) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (j <= 1.85e-39) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1 + (-4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (j <= (-2.9d+226)) then
        tmp = t_1 + (b * c)
    else if (j <= (-2.5d+74)) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if (j <= 1.85d-39) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t_1 + ((-4.0d0) * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -2.9e+226) {
		tmp = t_1 + (b * c);
	} else if (j <= -2.5e+74) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (j <= 1.85e-39) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1 + (-4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if j <= -2.9e+226:
		tmp = t_1 + (b * c)
	elif j <= -2.5e+74:
		tmp = t_1 + (t * (a * -4.0))
	elif j <= 1.85e-39:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t_1 + (-4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -2.9e+226)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (j <= -2.5e+74)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (j <= 1.85e-39)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -2.9e+226)
		tmp = t_1 + (b * c);
	elseif (j <= -2.5e+74)
		tmp = t_1 + (t * (a * -4.0));
	elseif (j <= 1.85e-39)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t_1 + (-4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+226], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.5e+74], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e-39], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.89999999999999974e226

   1. Initial program 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in b around inf 91.8%

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

   if -2.89999999999999974e226 < j < -2.49999999999999982e74

   1. Initial program 93.5%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in a around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*r* 72.7%

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

      4. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if -2.49999999999999982e74 < j < 1.85000000000000007e-39

   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. Taylor expanded in t around 0 59.6%

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

   3. Taylor expanded in j around 0 53.6%

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

   if 1.85000000000000007e-39 < j

   1. Initial program 86.8%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in i around inf 50.2%

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

      1. *-commutative 50.2%

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

   6. Simplified 50.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+226}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-39}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 18: 46.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+128} \lor \neg \left(i \leq 1.9 \cdot 10^{+227}\right) \land i \leq 1.2 \cdot 10^{+284}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \end{array} \]

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 (or (<= i -2.9e+128) (and (not (<= i 1.9e+227)) (<= i 1.2e+284)))
   (* x (* -4.0 i))
   (+ (* 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 ((i <= -2.9e+128) || (!(i <= 1.9e+227) && (i <= 1.2e+284))) {
		tmp = x * (-4.0 * i);
	} else {
		tmp = (j * (k * -27.0)) + (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 ((i <= (-2.9d+128)) .or. (.not. (i <= 1.9d+227)) .and. (i <= 1.2d+284)) then
        tmp = x * ((-4.0d0) * i)
    else
        tmp = (j * (k * (-27.0d0))) + (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 ((i <= -2.9e+128) || (!(i <= 1.9e+227) && (i <= 1.2e+284))) {
		tmp = x * (-4.0 * i);
	} else {
		tmp = (j * (k * -27.0)) + (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 (i <= -2.9e+128) or (not (i <= 1.9e+227) and (i <= 1.2e+284)):
		tmp = x * (-4.0 * i)
	else:
		tmp = (j * (k * -27.0)) + (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 ((i <= -2.9e+128) || (!(i <= 1.9e+227) && (i <= 1.2e+284)))
		tmp = Float64(x * Float64(-4.0 * i));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + 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 ((i <= -2.9e+128) || (~((i <= 1.9e+227)) && (i <= 1.2e+284)))
		tmp = x * (-4.0 * i);
	else
		tmp = (j * (k * -27.0)) + (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[Or[LessEqual[i, -2.9e+128], And[N[Not[LessEqual[i, 1.9e+227]], $MachinePrecision], LessEqual[i, 1.2e+284]]], N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.9e128 or 1.90000000000000018e227 < i < 1.2e284

   1. Initial program 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around inf 74.4%

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

   5. Taylor expanded in t around 0 70.7%

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

   if -2.9e128 < i < 1.90000000000000018e227 or 1.2e284 < i

   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 92.2%

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

   4. Taylor expanded in b around inf 52.6%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+128} \lor \neg \left(i \leq 1.9 \cdot 10^{+227}\right) \land i \leq 1.2 \cdot 10^{+284}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]

Alternative 19: 51.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -5.9 \cdot 10^{+50} \lor \neg \left(j \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (<= j -5.9e+50) (not (<= j 9e-22)))
   (+ (* j (* k -27.0)) (* b c))
   (- (* 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 ((j <= -5.9e+50) || !(j <= 9e-22)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) - (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 ((j <= (-5.9d+50)) .or. (.not. (j <= 9d-22))) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = (b * c) - (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 ((j <= -5.9e+50) || !(j <= 9e-22)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) - (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 (j <= -5.9e+50) or not (j <= 9e-22):
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = (b * c) - (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 ((j <= -5.9e+50) || !(j <= 9e-22))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = Float64(Float64(b * c) - 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 ((j <= -5.9e+50) || ~((j <= 9e-22)))
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = (b * c) - (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[j, -5.9e+50], N[Not[LessEqual[j, 9e-22]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.8999999999999998e50 or 8.99999999999999973e-22 < j

   1. Initial program 87.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in b around inf 59.9%

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

   if -5.8999999999999998e50 < j < 8.99999999999999973e-22

   1. Initial program 87.4%

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

   2. Taylor expanded in t around 0 60.5%

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

   3. Taylor expanded in j around 0 54.4%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.9 \cdot 10^{+50} \lor \neg \left(j \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 20: 51.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+127} \lor \neg \left(i \leq 1.4 \cdot 10^{+126}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -6.5e+127) (not (<= i 1.4e+126)))
   (- (* b c) (* 4.0 (* x i)))
   (- (* 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 ((i <= -6.5e+127) || !(i <= 1.4e+126)) {
		tmp = (b * c) - (4.0 * (x * i));
	} 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 ((i <= (-6.5d+127)) .or. (.not. (i <= 1.4d+126))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    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 ((i <= -6.5e+127) || !(i <= 1.4e+126)) {
		tmp = (b * c) - (4.0 * (x * i));
	} 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 (i <= -6.5e+127) or not (i <= 1.4e+126):
		tmp = (b * c) - (4.0 * (x * i))
	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 ((i <= -6.5e+127) || !(i <= 1.4e+126))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	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 ((i <= -6.5e+127) || ~((i <= 1.4e+126)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -6.5e+127], N[Not[LessEqual[i, 1.4e+126]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.5e127 or 1.40000000000000005e126 < i

   1. Initial program 83.4%

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

   2. Taylor expanded in t around 0 81.6%

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

   3. Taylor expanded in j around 0 76.3%

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

   if -6.5e127 < i < 1.40000000000000005e126

   1. Initial program 89.3%

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

   2. Taylor expanded in t around 0 58.4%

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

   3. Taylor expanded in i around 0 52.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.5 \cdot 10^{+127} \lor \neg \left(i \leq 1.4 \cdot 10^{+126}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 21: 32.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-60}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -4.8e-60)
   (* b c)
   (if (<= c 9.5e-117)
     (* -27.0 (* j k))
     (if (<= c 2.8e+114) (* t (* a -4.0)) (* 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 (c <= -4.8e-60) {
		tmp = b * c;
	} else if (c <= 9.5e-117) {
		tmp = -27.0 * (j * k);
	} else if (c <= 2.8e+114) {
		tmp = t * (a * -4.0);
	} 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 (c <= (-4.8d-60)) then
        tmp = b * c
    else if (c <= 9.5d-117) then
        tmp = (-27.0d0) * (j * k)
    else if (c <= 2.8d+114) then
        tmp = t * (a * (-4.0d0))
    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 (c <= -4.8e-60) {
		tmp = b * c;
	} else if (c <= 9.5e-117) {
		tmp = -27.0 * (j * k);
	} else if (c <= 2.8e+114) {
		tmp = t * (a * -4.0);
	} 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 c <= -4.8e-60:
		tmp = b * c
	elif c <= 9.5e-117:
		tmp = -27.0 * (j * k)
	elif c <= 2.8e+114:
		tmp = t * (a * -4.0)
	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 (c <= -4.8e-60)
		tmp = Float64(b * c);
	elseif (c <= 9.5e-117)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (c <= 2.8e+114)
		tmp = Float64(t * Float64(a * -4.0));
	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 (c <= -4.8e-60)
		tmp = b * c;
	elseif (c <= 9.5e-117)
		tmp = -27.0 * (j * k);
	elseif (c <= 2.8e+114)
		tmp = t * (a * -4.0);
	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[c, -4.8e-60], N[(b * c), $MachinePrecision], If[LessEqual[c, 9.5e-117], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e+114], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.80000000000000019e-60 or 2.8e114 < c

   1. Initial program 86.4%

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

   3. Simplified 90.7%

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

      1. associate-*r* 91.5%

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

      2. distribute-rgt-out-- 86.4%

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

      3. cancel-sign-sub-inv 86.4%

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

      4. associate-*l* 84.8%

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

      5. fma-def 87.3%

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

      6. associate-*l* 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in b around inf 42.3%

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

   if -4.80000000000000019e-60 < c < 9.5000000000000004e-117

   1. Initial program 89.1%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in j around inf 30.4%

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

   if 9.5000000000000004e-117 < c < 2.8e114

   1. Initial program 87.0%

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

   3. Simplified 89.2%

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

      1. associate-*r* 86.9%

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

      2. distribute-rgt-out-- 86.9%

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

      3. cancel-sign-sub-inv 86.9%

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

      4. associate-*l* 80.4%

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

      5. fma-def 80.4%

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

      6. associate-*l* 80.4%

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

   5. Applied egg-rr 80.4%

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

      1. fma-udef 80.4%

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

      2. *-commutative 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. metadata-eval 80.4%

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

   7. Applied egg-rr 80.4%

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

      1. +-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. associate-*r* 86.9%

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

      5. distribute-rgt-out 86.9%

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

   9. Simplified 86.9%

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

   10. Taylor expanded in a around inf 29.8%

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

       1. associate-*r* 29.8%

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

       2. *-commutative 29.8%

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

   12. Simplified 29.8%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-60}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22: 32.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -5.7 \cdot 10^{-52} \lor \neg \left(c \leq 1.06 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= c -5.7e-52) (not (<= c 1.06e+118))) (* 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 ((c <= -5.7e-52) || !(c <= 1.06e+118)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((c <= (-5.7d-52)) .or. (.not. (c <= 1.06d+118))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((c <= -5.7e-52) || !(c <= 1.06e+118)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c <= -5.7e-52) or not (c <= 1.06e+118):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((c <= -5.7e-52) || !(c <= 1.06e+118))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c <= -5.7e-52) || ~((c <= 1.06e+118)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[c, -5.7e-52], N[Not[LessEqual[c, 1.06e+118]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.6999999999999997e-52 or 1.06e118 < c

   1. Initial program 86.2%

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

   3. Simplified 90.6%

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

      1. associate-*r* 91.3%

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

      2. distribute-rgt-out-- 86.1%

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

      3. cancel-sign-sub-inv 86.1%

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

      4. associate-*l* 84.5%

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

      5. fma-def 87.1%

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

      6. associate-*l* 87.1%

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

   5. Applied egg-rr 87.1%

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

   6. Taylor expanded in b around inf 43.0%

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

   if -5.6999999999999997e-52 < c < 1.06e118

   1. Initial program 88.6%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in j around inf 27.8%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.7 \cdot 10^{-52} \lor \neg \left(c \leq 1.06 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 23: 24.0% 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 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 90.3%

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

   1. associate-*r* 90.6%

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

   2. distribute-rgt-out-- 87.1%

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

   3. cancel-sign-sub-inv 87.1%

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

   4. associate-*l* 84.8%

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

   5. fma-def 86.0%

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

   6. associate-*l* 86.0%

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

5. Applied egg-rr 86.0%

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

6. Taylor expanded in b around inf 25.3%

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

7. Final simplification 25.3%

   \[\leadsto b \cdot c \]

Developer target: 89.9% accurate, 0.9× 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 2023332 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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