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

Percentage Accurate: 85.1% → 92.2%

Time: 19.4s

Alternatives: 21

Speedup: 0.9×

• 50.0% 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: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-30} \lor \neg \left(t \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2e-30) (not (<= t 2e-75)))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
    (* j (* k -27.0)))
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2e-30) || !(t <= 2e-75)) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + (j * (k * -27.0));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2e-30) || !(t <= 2e-75))
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2e-30], N[Not[LessEqual[t, 2e-75]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e-30 or 1.9999999999999999e-75 < t

   1. Initial program 86.4%

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

   3. Simplified 93.8%

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

   if -2e-30 < t < 1.9999999999999999e-75

   1. Initial program 89.4%

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

      1. pow1 89.4%

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

      2. associate-*l* 94.5%

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

      3. *-commutative 94.5%

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

   4. Applied egg-rr 94.5%

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

      1. unpow1 94.5%

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

      2. associate-*l* 97.6%

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

      3. *-commutative 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-30} \lor \neg \left(t \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot 4\right)\\ t_2 := t \cdot \left(a \cdot 4\right)\\ t_3 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t\_2\right)\right) - t\_1\\ t_4 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t\_2\right) + b \cdot c\right) - t\_1\right) - t\_4\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3 - t\_4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

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 (* i (* x 4.0)))
        (t_2 (* t (* a 4.0)))
        (t_3 (- (+ (* b c) (- (* t (* z (* y (* x 18.0)))) t_2)) t_1))
        (t_4 (* k (* j 27.0))))
   (if (<= t_3 (- INFINITY))
     (- (- (+ (- (* y (* (* x 18.0) (* t z))) t_2) (* b c)) t_1) t_4)
     (if (<= t_3 INFINITY)
       (- t_3 t_4)
       (* 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 = i * (x * 4.0);
	double t_2 = t * (a * 4.0);
	double t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - t_2)) - t_1;
	double t_4 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - t_2) + (b * c)) - t_1) - t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3 - t_4;
	} 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 = i * (x * 4.0);
	double t_2 = t * (a * 4.0);
	double t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - t_2)) - t_1;
	double t_4 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - t_2) + (b * c)) - t_1) - t_4;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3 - t_4;
	} 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 = i * (x * 4.0)
	t_2 = t * (a * 4.0)
	t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - t_2)) - t_1
	t_4 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((((y * ((x * 18.0) * (t * z))) - t_2) + (b * c)) - t_1) - t_4
	elif t_3 <= math.inf:
		tmp = t_3 - t_4
	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(i * Float64(x * 4.0))
	t_2 = Float64(t * Float64(a * 4.0))
	t_3 = Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - t_2)) - t_1)
	t_4 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - t_2) + Float64(b * c)) - t_1) - t_4);
	elseif (t_3 <= Inf)
		tmp = Float64(t_3 - t_4);
	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 = i * (x * 4.0);
	t_2 = t * (a * 4.0);
	t_3 = ((b * c) + ((t * (z * (y * (x * 18.0)))) - t_2)) - t_1;
	t_4 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((((y * ((x * 18.0) * (t * z))) - t_2) + (b * c)) - t_1) - t_4;
	elseif (t_3 <= Inf)
		tmp = t_3 - t_4;
	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[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$3 - t$95$4), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.7%

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

      1. pow1 79.7%

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

      2. associate-*l* 87.7%

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

      3. *-commutative 87.7%

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

   4. Applied egg-rr 87.7%

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

      1. unpow1 87.7%

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

      2. associate-*l* 95.6%

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

      3. *-commutative 95.6%

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

   6. Simplified 95.6%

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

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

   1. Initial program 96.9%

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

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

   1. Initial program 0.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in x around inf 75.0%

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

4. Final simplification 95.3%

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

Alternative 3: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-23} \lor \neg \left(t \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1e-23) (not (<= t 2e-47)))
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1e-23) || !(t <= 2e-47)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1d-23)) .or. (.not. (t <= 2d-47))) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = ((((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0))) + (b * c)) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1e-23) || !(t <= 2e-47)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1e-23) or not (t <= 2e-47):
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1e-23) || !(t <= 2e-47))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1e-23) || ~((t <= 2e-47)))
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1e-23], N[Not[LessEqual[t, 2e-47]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999996e-24 or 1.9999999999999999e-47 < t

   1. Initial program 85.7%

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

   3. Simplified 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. Add Preprocessing

   if -9.9999999999999996e-24 < t < 1.9999999999999999e-47

   1. Initial program 90.0%

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

      1. pow1 90.0%

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

      2. associate-*l* 94.8%

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

      3. *-commutative 94.8%

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

   4. Applied egg-rr 94.8%

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

      1. unpow1 94.8%

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

      2. associate-*l* 97.7%

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

      3. *-commutative 97.7%

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

   6. Simplified 97.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-23} \lor \neg \left(t \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+242}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -5e+242)
     (+ (* j (* k -27.0)) (* b c))
     (if (<= t_1 2e+20)
       (-
        (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (* 4.0 (* x i)))
       (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -5e+242) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 2e+20) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-5d+242)) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (t_1 <= 2d+20) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -5e+242) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 2e+20) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -5e+242:
		tmp = (j * (k * -27.0)) + (b * c)
	elif t_1 <= 2e+20:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -5e+242)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (t_1 <= 2e+20)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -5e+242)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (t_1 <= 2e+20)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+242], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+20], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000004e242

   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 95.3%

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

   5. Taylor expanded in b around inf 99.9%

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

   if -5.0000000000000004e242 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e20

   1. Initial program 91.0%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in j around 0 86.8%

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

   if 2e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. distribute-lft-out 83.3%

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

      2. *-commutative 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+242}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-96}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+173}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

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 (* k (* j 27.0)))
        (t_2 (* x (- (* (* t y) (* 18.0 z)) (* i 4.0)))))
   (if (<= x -3.2e+34)
     t_2
     (if (<= x 1.5e-96)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= x 7.4e+33)
         (- (- (* b c) (* 4.0 (* x i))) t_1)
         (if (<= x 4.2e+142)
           t_2
           (if (<= x 5.3e+173)
             (- (* -4.0 (+ (* x i) (* t a))) 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 = k * (j * 27.0);
	double t_2 = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	double tmp;
	if (x <= -3.2e+34) {
		tmp = t_2;
	} else if (x <= 1.5e-96) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 7.4e+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 4.2e+142) {
		tmp = t_2;
	} else if (x <= 5.3e+173) {
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = x * (((t * y) * (18.0d0 * z)) - (i * 4.0d0))
    if (x <= (-3.2d+34)) then
        tmp = t_2
    else if (x <= 1.5d-96) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 7.4d+33) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (x <= 4.2d+142) then
        tmp = t_2
    else if (x <= 5.3d+173) then
        tmp = ((-4.0d0) * ((x * i) + (t * a))) - t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	double tmp;
	if (x <= -3.2e+34) {
		tmp = t_2;
	} else if (x <= 1.5e-96) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 7.4e+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 4.2e+142) {
		tmp = t_2;
	} else if (x <= 5.3e+173) {
		tmp = (-4.0 * ((x * i) + (t * a))) - 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 = k * (j * 27.0)
	t_2 = x * (((t * y) * (18.0 * z)) - (i * 4.0))
	tmp = 0
	if x <= -3.2e+34:
		tmp = t_2
	elif x <= 1.5e-96:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 7.4e+33:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif x <= 4.2e+142:
		tmp = t_2
	elif x <= 5.3e+173:
		tmp = (-4.0 * ((x * i) + (t * a))) - 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(k * Float64(j * 27.0))
	t_2 = Float64(x * Float64(Float64(Float64(t * y) * Float64(18.0 * z)) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -3.2e+34)
		tmp = t_2;
	elseif (x <= 1.5e-96)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 7.4e+33)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= 4.2e+142)
		tmp = t_2;
	elseif (x <= 5.3e+173)
		tmp = Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) - 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 = k * (j * 27.0);
	t_2 = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	tmp = 0.0;
	if (x <= -3.2e+34)
		tmp = t_2;
	elseif (x <= 1.5e-96)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 7.4e+33)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (x <= 4.2e+142)
		tmp = t_2;
	elseif (x <= 5.3e+173)
		tmp = (-4.0 * ((x * i) + (t * a))) - 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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+34], t$95$2, If[LessEqual[x, 1.5e-96], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 7.4e+33], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 4.2e+142], t$95$2, If[LessEqual[x, 5.3e+173], N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.1999999999999998e34 or 7.3999999999999997e33 < x < 4.2e142

   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 84.6%

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

   5. Taylor expanded in x around inf 76.1%

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

      1. pow1 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r* 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. unpow1 74.9%

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

      2. associate-*l* 74.9%

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

   9. Simplified 74.9%

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

   if -3.1999999999999998e34 < x < 1.5e-96

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 80.3%

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

   if 1.5e-96 < x < 7.3999999999999997e33

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0 75.3%

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

   if 4.2e142 < x < 5.29999999999999999e173

   1. Initial program 55.6%

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

      1. pow1 55.6%

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

      2. associate-*l* 55.6%

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

      3. *-commutative 55.6%

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

   4. Applied egg-rr 55.6%

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

      1. unpow1 55.6%

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

      2. associate-*l* 66.7%

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

      3. *-commutative 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in b around 0 100.0%

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

   if 5.29999999999999999e173 < x

   1. Initial program 78.5%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 87.6%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-96}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+173}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ t_3 := j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.68 \cdot 10^{-124}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (- (- (* b c) (* 4.0 (* x i))) t_1))
        (t_3
         (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))))
   (if (<= t -2e-17)
     t_3
     (if (<= t -1.5e-36)
       t_2
       (if (<= t -1.68e-124)
         (- (* -4.0 (+ (* x i) (* t a))) t_1)
         (if (<= t 2.1e-24) t_2 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double t_3 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -2e-17) {
		tmp = t_3;
	} else if (t <= -1.5e-36) {
		tmp = t_2;
	} else if (t <= -1.68e-124) {
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	} else if (t <= 2.1e-24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = k * (j * 27.0d0)
    t_2 = ((b * c) - (4.0d0 * (x * i))) - t_1
    t_3 = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    if (t <= (-2d-17)) then
        tmp = t_3
    else if (t <= (-1.5d-36)) then
        tmp = t_2
    else if (t <= (-1.68d-124)) then
        tmp = ((-4.0d0) * ((x * i) + (t * a))) - t_1
    else if (t <= 2.1d-24) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double t_3 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -2e-17) {
		tmp = t_3;
	} else if (t <= -1.5e-36) {
		tmp = t_2;
	} else if (t <= -1.68e-124) {
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	} else if (t <= 2.1e-24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1
	t_3 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	tmp = 0
	if t <= -2e-17:
		tmp = t_3
	elif t <= -1.5e-36:
		tmp = t_2
	elif t <= -1.68e-124:
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1
	elif t <= 2.1e-24:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1)
	t_3 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -2e-17)
		tmp = t_3;
	elseif (t <= -1.5e-36)
		tmp = t_2;
	elseif (t <= -1.68e-124)
		tmp = Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) - t_1);
	elseif (t <= 2.1e-24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	t_3 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -2e-17)
		tmp = t_3;
	elseif (t <= -1.5e-36)
		tmp = t_2;
	elseif (t <= -1.68e-124)
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	elseif (t <= 2.1e-24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-17], t$95$3, If[LessEqual[t, -1.5e-36], t$95$2, If[LessEqual[t, -1.68e-124], N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.1e-24], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.00000000000000014e-17 or 2.0999999999999999e-24 < t

   1. Initial program 85.2%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 75.5%

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

   if -2.00000000000000014e-17 < t < -1.5000000000000001e-36 or -1.68e-124 < t < 2.0999999999999999e-24

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 86.3%

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

   if -1.5000000000000001e-36 < t < -1.68e-124

   1. Initial program 90.3%

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

      1. pow1 90.3%

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

      2. associate-*l* 95.0%

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

      3. *-commutative 95.0%

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

   4. Applied egg-rr 95.0%

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

      1. unpow1 95.0%

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

      2. associate-*l* 94.9%

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

      3. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. distribute-lft-out 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in b around 0 70.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -1.68 \cdot 10^{-124}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-24}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{x \cdot i}{c}\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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) 5e+218)
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (- (* c (+ b (* -4.0 (/ (* x i) c)))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= 5e+218) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (c * (b + (-4.0 * ((x * i) / c)))) - (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) <= 5d+218) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = (c * (b + ((-4.0d0) * ((x * i) / c)))) - (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) <= 5e+218) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (c * (b + (-4.0 * ((x * i) / c)))) - (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) <= 5e+218:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = (c * (b + (-4.0 * ((x * i) / c)))) - (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) <= 5e+218)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(x * i) / c)))) - 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) <= 5e+218)
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = (c * (b + (-4.0 * ((x * i) / c)))) - (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], 5e+218], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(b + N[(-4.0 * N[(N[(x * i), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 4.99999999999999983e218

   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 89.9%

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

   if 4.99999999999999983e218 < (*.f64 b c)

   1. Initial program 78.3%

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

   3. Taylor expanded in t around 0 87.0%

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

   4. Taylor expanded in c around inf 95.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{x \cdot i}{c}\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 122:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+143} \lor \neg \left(x \leq 5 \cdot 10^{+173}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= x -5e+34)
     (* x (- (* (* t y) (* 18.0 z)) (* i 4.0)))
     (if (<= x 122.0)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (or (<= x 2.4e+143) (not (<= x 5e+173)))
         (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
         (- (* -4.0 (+ (* x i) (* t a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (x <= -5e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= 122.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if ((x <= 2.4e+143) || !(x <= 5e+173)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (x <= (-5d+34)) then
        tmp = x * (((t * y) * (18.0d0 * z)) - (i * 4.0d0))
    else if (x <= 122.0d0) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if ((x <= 2.4d+143) .or. (.not. (x <= 5d+173))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else
        tmp = ((-4.0d0) * ((x * i) + (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (x <= -5e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= 122.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if ((x <= 2.4e+143) || !(x <= 5e+173)) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else {
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if x <= -5e+34:
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0))
	elif x <= 122.0:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif (x <= 2.4e+143) or not (x <= 5e+173):
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	else:
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (x <= -5e+34)
		tmp = Float64(x * Float64(Float64(Float64(t * y) * Float64(18.0 * z)) - Float64(i * 4.0)));
	elseif (x <= 122.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif ((x <= 2.4e+143) || !(x <= 5e+173))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (x <= -5e+34)
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	elseif (x <= 122.0)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif ((x <= 2.4e+143) || ~((x <= 5e+173)))
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	else
		tmp = (-4.0 * ((x * i) + (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+34], N[(x * N[(N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 122.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[Or[LessEqual[x, 2.4e+143], N[Not[LessEqual[x, 5e+173]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.9999999999999998e34

   1. Initial program 76.8%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. pow1 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*r* 75.2%

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

   7. Applied egg-rr 75.2%

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

      1. unpow1 75.2%

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

      2. associate-*l* 75.2%

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

   9. Simplified 75.2%

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

   if -4.9999999999999998e34 < x < 122

   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. Add Preprocessing

   3. Taylor expanded in x around 0 76.8%

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

   if 122 < x < 2.3999999999999998e143 or 5.00000000000000034e173 < x

   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 88.6%

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

   5. Taylor expanded in x around inf 81.0%

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

   if 2.3999999999999998e143 < x < 5.00000000000000034e173

   1. Initial program 55.6%

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

      1. pow1 55.6%

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

      2. associate-*l* 55.6%

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

      3. *-commutative 55.6%

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

   4. Applied egg-rr 55.6%

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

      1. unpow1 55.6%

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

      2. associate-*l* 66.7%

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

      3. *-commutative 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in b around 0 100.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 122:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+143} \lor \neg \left(x \leq 5 \cdot 10^{+173}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-200}:\\ \;\;\;\;t\_2 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-95}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_2 (* j (* k -27.0))))
   (if (<= t -1.12e+35)
     t_1
     (if (<= t 1.85e-200)
       (+ t_2 (* i (* x -4.0)))
       (if (<= t 2.55e-95)
         (+ t_2 (* b c))
         (if (<= t 2e+17) (- (* x (* -4.0 i)) (* k (* j 27.0))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (t <= -1.12e+35) {
		tmp = t_1;
	} else if (t <= 1.85e-200) {
		tmp = t_2 + (i * (x * -4.0));
	} else if (t <= 2.55e-95) {
		tmp = t_2 + (b * c);
	} else if (t <= 2e+17) {
		tmp = (x * (-4.0 * i)) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_2 = j * (k * (-27.0d0))
    if (t <= (-1.12d+35)) then
        tmp = t_1
    else if (t <= 1.85d-200) then
        tmp = t_2 + (i * (x * (-4.0d0)))
    else if (t <= 2.55d-95) then
        tmp = t_2 + (b * c)
    else if (t <= 2d+17) then
        tmp = (x * ((-4.0d0) * i)) - (k * (j * 27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (t <= -1.12e+35) {
		tmp = t_1;
	} else if (t <= 1.85e-200) {
		tmp = t_2 + (i * (x * -4.0));
	} else if (t <= 2.55e-95) {
		tmp = t_2 + (b * c);
	} else if (t <= 2e+17) {
		tmp = (x * (-4.0 * i)) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if t <= -1.12e+35:
		tmp = t_1
	elif t <= 1.85e-200:
		tmp = t_2 + (i * (x * -4.0))
	elif t <= 2.55e-95:
		tmp = t_2 + (b * c)
	elif t <= 2e+17:
		tmp = (x * (-4.0 * i)) - (k * (j * 27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -1.12e+35)
		tmp = t_1;
	elseif (t <= 1.85e-200)
		tmp = Float64(t_2 + Float64(i * Float64(x * -4.0)));
	elseif (t <= 2.55e-95)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (t <= 2e+17)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) - Float64(k * Float64(j * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -1.12e+35)
		tmp = t_1;
	elseif (t <= 1.85e-200)
		tmp = t_2 + (i * (x * -4.0));
	elseif (t <= 2.55e-95)
		tmp = t_2 + (b * c);
	elseif (t <= 2e+17)
		tmp = (x * (-4.0 * i)) - (k * (j * 27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e+35], t$95$1, If[LessEqual[t, 1.85e-200], N[(t$95$2 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-95], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+17], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.12000000000000003e35 or 2e17 < t

   1. Initial program 85.7%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 77.6%

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

   6. Taylor expanded in t around inf 68.4%

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

   if -1.12000000000000003e35 < t < 1.85000000000000005e-200

   1. Initial program 88.7%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in i around inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*r* 55.7%

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

      4. *-commutative 55.7%

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

      5. *-commutative 55.7%

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

   7. Simplified 55.7%

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

   if 1.85000000000000005e-200 < t < 2.55e-95

   1. Initial program 95.4%

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

   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. Add Preprocessing

   5. Taylor expanded in b around inf 69.3%

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

   if 2.55e-95 < t < 2e17

   1. Initial program 84.9%

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

      1. pow1 84.9%

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

      2. associate-*l* 88.3%

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

      3. *-commutative 88.3%

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

   4. Applied egg-rr 88.3%

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

      1. unpow1 88.3%

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

      2. associate-*l* 81.3%

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

      3. *-commutative 81.3%

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

   6. Simplified 81.3%

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

   7. Taylor expanded in i around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-*r* 69.7%

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

   9. Simplified 69.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-200}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+157}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))) (t_2 (* k (* j -27.0))))
   (if (<= b -7.6e+157)
     (* b c)
     (if (<= b -6.3e+63)
       t_1
       (if (<= b -6e+22)
         t_2
         (if (<= b -1.55e-281) t_1 (if (<= b 1e-18) 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 = -4.0 * (x * i);
	double t_2 = k * (j * -27.0);
	double tmp;
	if (b <= -7.6e+157) {
		tmp = b * c;
	} else if (b <= -6.3e+63) {
		tmp = t_1;
	} else if (b <= -6e+22) {
		tmp = t_2;
	} else if (b <= -1.55e-281) {
		tmp = t_1;
	} else if (b <= 1e-18) {
		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 = (-4.0d0) * (x * i)
    t_2 = k * (j * (-27.0d0))
    if (b <= (-7.6d+157)) then
        tmp = b * c
    else if (b <= (-6.3d+63)) then
        tmp = t_1
    else if (b <= (-6d+22)) then
        tmp = t_2
    else if (b <= (-1.55d-281)) then
        tmp = t_1
    else if (b <= 1d-18) 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 = -4.0 * (x * i);
	double t_2 = k * (j * -27.0);
	double tmp;
	if (b <= -7.6e+157) {
		tmp = b * c;
	} else if (b <= -6.3e+63) {
		tmp = t_1;
	} else if (b <= -6e+22) {
		tmp = t_2;
	} else if (b <= -1.55e-281) {
		tmp = t_1;
	} else if (b <= 1e-18) {
		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 = -4.0 * (x * i)
	t_2 = k * (j * -27.0)
	tmp = 0
	if b <= -7.6e+157:
		tmp = b * c
	elif b <= -6.3e+63:
		tmp = t_1
	elif b <= -6e+22:
		tmp = t_2
	elif b <= -1.55e-281:
		tmp = t_1
	elif b <= 1e-18:
		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(-4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (b <= -7.6e+157)
		tmp = Float64(b * c);
	elseif (b <= -6.3e+63)
		tmp = t_1;
	elseif (b <= -6e+22)
		tmp = t_2;
	elseif (b <= -1.55e-281)
		tmp = t_1;
	elseif (b <= 1e-18)
		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 = -4.0 * (x * i);
	t_2 = k * (j * -27.0);
	tmp = 0.0;
	if (b <= -7.6e+157)
		tmp = b * c;
	elseif (b <= -6.3e+63)
		tmp = t_1;
	elseif (b <= -6e+22)
		tmp = t_2;
	elseif (b <= -1.55e-281)
		tmp = t_1;
	elseif (b <= 1e-18)
		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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+157], N[(b * c), $MachinePrecision], If[LessEqual[b, -6.3e+63], t$95$1, If[LessEqual[b, -6e+22], t$95$2, If[LessEqual[b, -1.55e-281], t$95$1, If[LessEqual[b, 1e-18], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.6000000000000002e157 or 1.0000000000000001e-18 < b

   1. Initial program 82.5%

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

      1. pow1 82.5%

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

      2. associate-*l* 82.5%

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

      3. *-commutative 82.5%

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

   4. Applied egg-rr 82.5%

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

      1. unpow1 82.5%

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

      2. associate-*l* 81.6%

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

      3. *-commutative 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in b around inf 56.5%

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

   8. Taylor expanded in j around inf 54.3%

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

      1. cancel-sign-sub-inv 54.3%

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

      2. associate-/l* 54.3%

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

      3. metadata-eval 54.3%

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

      4. *-commutative 54.3%

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

   10. Simplified 54.3%

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

   11. Taylor expanded in j around 0 40.5%

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

   if -7.6000000000000002e157 < b < -6.2999999999999998e63 or -6e22 < b < -1.5500000000000001e-281

   1. Initial program 88.1%

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

      1. pow1 88.1%

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

      2. associate-*l* 89.7%

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

      3. *-commutative 89.7%

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

   4. Applied egg-rr 89.7%

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

      1. unpow1 89.7%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in y around 0 78.4%

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

      1. distribute-lft-out 78.4%

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

      2. *-commutative 78.4%

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

      3. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in b around 0 69.5%

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

   11. Taylor expanded in i around inf 36.4%

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

       1. *-commutative 36.4%

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

   13. Simplified 36.4%

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

   if -6.2999999999999998e63 < b < -6e22 or -1.5500000000000001e-281 < b < 1.0000000000000001e-18

   1. Initial program 93.8%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in j around inf 31.3%

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

      1. metadata-eval 31.3%

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

      2. distribute-lft-neg-in 31.3%

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

      3. associate-*r* 31.4%

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

      4. *-commutative 31.4%

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

      5. distribute-rgt-neg-in 31.4%

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

      6. distribute-lft-neg-in 31.4%

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

      7. metadata-eval 31.4%

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

   7. Simplified 31.4%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+157}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+22}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-281}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{-18}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* x i) (* t a)))) (t_2 (+ (* j (* k -27.0)) (* b c))))
   (if (<= c -4.5e-28)
     t_2
     (if (<= c -2.05e-265)
       t_1
       (if (<= c 3.8e-260)
         (* z (* (* x 18.0) (* t y)))
         (if (<= c 7.5e+36) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (t * a));
	double t_2 = (j * (k * -27.0)) + (b * c);
	double tmp;
	if (c <= -4.5e-28) {
		tmp = t_2;
	} else if (c <= -2.05e-265) {
		tmp = t_1;
	} else if (c <= 3.8e-260) {
		tmp = z * ((x * 18.0) * (t * y));
	} else if (c <= 7.5e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * a))
    t_2 = (j * (k * (-27.0d0))) + (b * c)
    if (c <= (-4.5d-28)) then
        tmp = t_2
    else if (c <= (-2.05d-265)) then
        tmp = t_1
    else if (c <= 3.8d-260) then
        tmp = z * ((x * 18.0d0) * (t * y))
    else if (c <= 7.5d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (t * a));
	double t_2 = (j * (k * -27.0)) + (b * c);
	double tmp;
	if (c <= -4.5e-28) {
		tmp = t_2;
	} else if (c <= -2.05e-265) {
		tmp = t_1;
	} else if (c <= 3.8e-260) {
		tmp = z * ((x * 18.0) * (t * y));
	} else if (c <= 7.5e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((x * i) + (t * a))
	t_2 = (j * (k * -27.0)) + (b * c)
	tmp = 0
	if c <= -4.5e-28:
		tmp = t_2
	elif c <= -2.05e-265:
		tmp = t_1
	elif c <= 3.8e-260:
		tmp = z * ((x * 18.0) * (t * y))
	elif c <= 7.5e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	tmp = 0.0
	if (c <= -4.5e-28)
		tmp = t_2;
	elseif (c <= -2.05e-265)
		tmp = t_1;
	elseif (c <= 3.8e-260)
		tmp = Float64(z * Float64(Float64(x * 18.0) * Float64(t * y)));
	elseif (c <= 7.5e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((x * i) + (t * a));
	t_2 = (j * (k * -27.0)) + (b * c);
	tmp = 0.0;
	if (c <= -4.5e-28)
		tmp = t_2;
	elseif (c <= -2.05e-265)
		tmp = t_1;
	elseif (c <= 3.8e-260)
		tmp = z * ((x * 18.0) * (t * y));
	elseif (c <= 7.5e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e-28], t$95$2, If[LessEqual[c, -2.05e-265], t$95$1, If[LessEqual[c, 3.8e-260], N[(z * N[(N[(x * 18.0), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.4999999999999998e-28 or 7.50000000000000054e36 < c

   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 90.2%

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

   5. Taylor expanded in b around inf 58.5%

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

   if -4.4999999999999998e-28 < c < -2.05e-265 or 3.8000000000000003e-260 < c < 7.50000000000000054e36

   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. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 89.3%

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

      2. associate-*l* 89.2%

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

      3. *-commutative 89.2%

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

   4. Applied egg-rr 89.2%

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

      1. unpow1 89.2%

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

      2. associate-*l* 90.1%

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

      3. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in b around 0 74.7%

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

   11. Taylor expanded in j around 0 60.3%

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

   if -2.05e-265 < c < 3.8000000000000003e-260

   1. Initial program 80.2%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in x around inf 68.7%

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

   6. Taylor expanded in z around inf 63.3%

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

   7. Taylor expanded in i around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r* 53.2%

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

      3. associate-*l* 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*l* 53.3%

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

      6. *-commutative 53.3%

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

   9. Simplified 53.3%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-265}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+36}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-290}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* x i) (* t a)))))
   (if (<= b -1.05e+205)
     (* b c)
     (if (<= b -9.5e-279)
       t_1
       (if (<= b 9e-290) (* -27.0 (* j k)) (if (<= b 1.9e-82) 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 = -4.0 * ((x * i) + (t * a));
	double tmp;
	if (b <= -1.05e+205) {
		tmp = b * c;
	} else if (b <= -9.5e-279) {
		tmp = t_1;
	} else if (b <= 9e-290) {
		tmp = -27.0 * (j * k);
	} else if (b <= 1.9e-82) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((x * i) + (t * a))
    if (b <= (-1.05d+205)) then
        tmp = b * c
    else if (b <= (-9.5d-279)) then
        tmp = t_1
    else if (b <= 9d-290) then
        tmp = (-27.0d0) * (j * k)
    else if (b <= 1.9d-82) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((x * i) + (t * a));
	double tmp;
	if (b <= -1.05e+205) {
		tmp = b * c;
	} else if (b <= -9.5e-279) {
		tmp = t_1;
	} else if (b <= 9e-290) {
		tmp = -27.0 * (j * k);
	} else if (b <= 1.9e-82) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((x * i) + (t * a))
	tmp = 0
	if b <= -1.05e+205:
		tmp = b * c
	elif b <= -9.5e-279:
		tmp = t_1
	elif b <= 9e-290:
		tmp = -27.0 * (j * k)
	elif b <= 1.9e-82:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)))
	tmp = 0.0
	if (b <= -1.05e+205)
		tmp = Float64(b * c);
	elseif (b <= -9.5e-279)
		tmp = t_1;
	elseif (b <= 9e-290)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (b <= 1.9e-82)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((x * i) + (t * a));
	tmp = 0.0;
	if (b <= -1.05e+205)
		tmp = b * c;
	elseif (b <= -9.5e-279)
		tmp = t_1;
	elseif (b <= 9e-290)
		tmp = -27.0 * (j * k);
	elseif (b <= 1.9e-82)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+205], N[(b * c), $MachinePrecision], If[LessEqual[b, -9.5e-279], t$95$1, If[LessEqual[b, 9e-290], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-82], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e205 or 1.9000000000000001e-82 < b

   1. Initial program 84.4%

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

      1. pow1 84.4%

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

      2. associate-*l* 84.4%

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

      3. *-commutative 84.4%

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

   4. Applied egg-rr 84.4%

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

      1. unpow1 84.4%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in b around inf 52.8%

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

   8. Taylor expanded in j around inf 50.0%

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

      1. cancel-sign-sub-inv 50.0%

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

      2. associate-/l* 49.9%

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

      3. metadata-eval 49.9%

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

      4. *-commutative 49.9%

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

   10. Simplified 49.9%

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

   11. Taylor expanded in j around 0 33.4%

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

   if -1.05e205 < b < -9.4999999999999996e-279 or 9e-290 < b < 1.9000000000000001e-82

   1. Initial program 89.0%

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

      1. pow1 89.0%

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

      2. associate-*l* 88.8%

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

      3. *-commutative 88.8%

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

   4. Applied egg-rr 88.8%

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

      1. unpow1 88.8%

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

      2. associate-*l* 88.5%

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

      3. *-commutative 88.5%

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

   6. Simplified 88.5%

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

   7. Taylor expanded in y around 0 78.4%

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

      1. distribute-lft-out 78.4%

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

      2. *-commutative 78.4%

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

      3. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in b around 0 67.1%

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

   11. Taylor expanded in j around 0 49.4%

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

   if -9.4999999999999996e-279 < b < 9e-290

   1. Initial program 99.5%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in j around inf 46.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-279}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-290}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-192}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

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
 (if (<= x -2.3e+34)
   (* x (- (* (* t y) (* 18.0 z)) (* i 4.0)))
   (if (<= x -2.1e-192)
     (- (* -4.0 (+ (* x i) (* t a))) (* k (* j 27.0)))
     (if (<= x 8e-98)
       (+ (* j (* k -27.0)) (* b c))
       (* 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 tmp;
	if (x <= -2.3e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= -2.1e-192) {
		tmp = (-4.0 * ((x * i) + (t * a))) - (k * (j * 27.0));
	} else if (x <= 8e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-2.3d+34)) then
        tmp = x * (((t * y) * (18.0d0 * z)) - (i * 4.0d0))
    else if (x <= (-2.1d-192)) then
        tmp = ((-4.0d0) * ((x * i) + (t * a))) - (k * (j * 27.0d0))
    else if (x <= 8d-98) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.3e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= -2.1e-192) {
		tmp = (-4.0 * ((x * i) + (t * a))) - (k * (j * 27.0));
	} else if (x <= 8e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} 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):
	tmp = 0
	if x <= -2.3e+34:
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0))
	elif x <= -2.1e-192:
		tmp = (-4.0 * ((x * i) + (t * a))) - (k * (j * 27.0))
	elif x <= 8e-98:
		tmp = (j * (k * -27.0)) + (b * c)
	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)
	tmp = 0.0
	if (x <= -2.3e+34)
		tmp = Float64(x * Float64(Float64(Float64(t * y) * Float64(18.0 * z)) - Float64(i * 4.0)));
	elseif (x <= -2.1e-192)
		tmp = Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif (x <= 8e-98)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	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)
	tmp = 0.0;
	if (x <= -2.3e+34)
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	elseif (x <= -2.1e-192)
		tmp = (-4.0 * ((x * i) + (t * a))) - (k * (j * 27.0));
	elseif (x <= 8e-98)
		tmp = (j * (k * -27.0)) + (b * c);
	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_] := If[LessEqual[x, -2.3e+34], N[(x * N[(N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-192], N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-98], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999998e34

   1. Initial program 76.8%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. pow1 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*r* 75.2%

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

   7. Applied egg-rr 75.2%

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

      1. unpow1 75.2%

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

      2. associate-*l* 75.2%

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

   9. Simplified 75.2%

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

   if -2.2999999999999998e34 < x < -2.09999999999999993e-192

   1. Initial program 95.2%

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

      1. pow1 95.2%

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

      2. associate-*l* 90.6%

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

      3. *-commutative 90.6%

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

   4. Applied egg-rr 90.6%

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

      1. unpow1 90.6%

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

      2. associate-*l* 90.9%

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

      3. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in y around 0 90.7%

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

      1. distribute-lft-out 90.7%

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

      2. *-commutative 90.7%

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

      3. *-commutative 90.7%

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

   9. Simplified 90.7%

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

   10. Taylor expanded in b around 0 77.1%

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

   if -2.09999999999999993e-192 < x < 7.99999999999999951e-98

   1. Initial program 95.7%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in b around inf 73.4%

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

   if 7.99999999999999951e-98 < x

   1. Initial program 84.2%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-192}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

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
 (if (<= x -4.8e+34)
   (* x (- (* (* t y) (* 18.0 z)) (* i 4.0)))
   (if (<= x -1.6e-144)
     (* -4.0 (+ (* x i) (* t a)))
     (if (<= x 5.1e-98)
       (+ (* j (* k -27.0)) (* b c))
       (* 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 tmp;
	if (x <= -4.8e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= -1.6e-144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (x <= 5.1e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-4.8d+34)) then
        tmp = x * (((t * y) * (18.0d0 * z)) - (i * 4.0d0))
    else if (x <= (-1.6d-144)) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (x <= 5.1d-98) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.8e+34) {
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	} else if (x <= -1.6e-144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (x <= 5.1e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} 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):
	tmp = 0
	if x <= -4.8e+34:
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0))
	elif x <= -1.6e-144:
		tmp = -4.0 * ((x * i) + (t * a))
	elif x <= 5.1e-98:
		tmp = (j * (k * -27.0)) + (b * c)
	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)
	tmp = 0.0
	if (x <= -4.8e+34)
		tmp = Float64(x * Float64(Float64(Float64(t * y) * Float64(18.0 * z)) - Float64(i * 4.0)));
	elseif (x <= -1.6e-144)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (x <= 5.1e-98)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	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)
	tmp = 0.0;
	if (x <= -4.8e+34)
		tmp = x * (((t * y) * (18.0 * z)) - (i * 4.0));
	elseif (x <= -1.6e-144)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (x <= 5.1e-98)
		tmp = (j * (k * -27.0)) + (b * c);
	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_] := If[LessEqual[x, -4.8e+34], N[(x * N[(N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-144], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-98], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.79999999999999974e34

   1. Initial program 76.8%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. pow1 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*r* 75.2%

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

   7. Applied egg-rr 75.2%

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

      1. unpow1 75.2%

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

      2. associate-*l* 75.2%

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

   9. Simplified 75.2%

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

   if -4.79999999999999974e34 < x < -1.59999999999999986e-144

   1. Initial program 94.0%

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

      1. pow1 94.0%

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

      2. associate-*l* 91.0%

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

      3. *-commutative 91.0%

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

   4. Applied egg-rr 91.0%

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

      1. unpow1 91.0%

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

      2. associate-*l* 91.4%

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

      3. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 88.3%

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

      1. distribute-lft-out 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

   9. Simplified 88.3%

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

   10. Taylor expanded in b around 0 71.1%

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

   11. Taylor expanded in j around 0 65.8%

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

   if -1.59999999999999986e-144 < x < 5.10000000000000022e-98

   1. Initial program 96.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in b around inf 71.5%

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

   if 5.10000000000000022e-98 < x

   1. Initial program 84.2%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))
   (if (<= x -2.5e+34)
     t_1
     (if (<= x -1.6e-144)
       (* -4.0 (+ (* x i) (* t a)))
       (if (<= x 8e-98) (+ (* j (* k -27.0)) (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.5e+34) {
		tmp = t_1;
	} else if (x <= -1.6e-144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (x <= 8e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    if (x <= (-2.5d+34)) then
        tmp = t_1
    else if (x <= (-1.6d-144)) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (x <= 8d-98) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.5e+34) {
		tmp = t_1;
	} else if (x <= -1.6e-144) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (x <= 8e-98) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	tmp = 0
	if x <= -2.5e+34:
		tmp = t_1
	elif x <= -1.6e-144:
		tmp = -4.0 * ((x * i) + (t * a))
	elif x <= 8e-98:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.5e+34)
		tmp = t_1;
	elseif (x <= -1.6e-144)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (x <= 8e-98)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.5e+34)
		tmp = t_1;
	elseif (x <= -1.6e-144)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (x <= 8e-98)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+34], t$95$1, If[LessEqual[x, -1.6e-144], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-98], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4999999999999999e34 or 7.99999999999999951e-98 < x

   1. Initial program 81.4%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around inf 72.1%

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

   if -2.4999999999999999e34 < x < -1.59999999999999986e-144

   1. Initial program 94.0%

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

      1. pow1 94.0%

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

      2. associate-*l* 91.0%

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

      3. *-commutative 91.0%

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

   4. Applied egg-rr 91.0%

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

      1. unpow1 91.0%

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

      2. associate-*l* 91.4%

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

      3. *-commutative 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 88.3%

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

      1. distribute-lft-out 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

   9. Simplified 88.3%

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

   10. Taylor expanded in b around 0 71.1%

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

   11. Taylor expanded in j around 0 65.8%

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

   if -1.59999999999999986e-144 < x < 7.99999999999999951e-98

   1. Initial program 96.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in b around inf 71.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-94}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-238}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-13}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= b -2.45e+151)
   (* b c)
   (if (<= b -8.2e-94)
     (* -27.0 (* j k))
     (if (<= b -6.8e-238)
       (* -4.0 (* t a))
       (if (<= b 7.6e-13) (* k (* j -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 <= -2.45e+151) {
		tmp = b * c;
	} else if (b <= -8.2e-94) {
		tmp = -27.0 * (j * k);
	} else if (b <= -6.8e-238) {
		tmp = -4.0 * (t * a);
	} else if (b <= 7.6e-13) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (b <= (-2.45d+151)) then
        tmp = b * c
    else if (b <= (-8.2d-94)) then
        tmp = (-27.0d0) * (j * k)
    else if (b <= (-6.8d-238)) then
        tmp = (-4.0d0) * (t * a)
    else if (b <= 7.6d-13) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -2.45e+151) {
		tmp = b * c;
	} else if (b <= -8.2e-94) {
		tmp = -27.0 * (j * k);
	} else if (b <= -6.8e-238) {
		tmp = -4.0 * (t * a);
	} else if (b <= 7.6e-13) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if b <= -2.45e+151:
		tmp = b * c
	elif b <= -8.2e-94:
		tmp = -27.0 * (j * k)
	elif b <= -6.8e-238:
		tmp = -4.0 * (t * a)
	elif b <= 7.6e-13:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= -2.45e+151)
		tmp = Float64(b * c);
	elseif (b <= -8.2e-94)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (b <= -6.8e-238)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (b <= 7.6e-13)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (b <= -2.45e+151)
		tmp = b * c;
	elseif (b <= -8.2e-94)
		tmp = -27.0 * (j * k);
	elseif (b <= -6.8e-238)
		tmp = -4.0 * (t * a);
	elseif (b <= 7.6e-13)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[b, -2.45e+151], N[(b * c), $MachinePrecision], If[LessEqual[b, -8.2e-94], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.8e-238], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e-13], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.45e151 or 7.5999999999999999e-13 < b

   1. Initial program 82.0%

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

      1. pow1 82.0%

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

      2. associate-*l* 82.0%

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

      3. *-commutative 82.0%

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

   4. Applied egg-rr 82.0%

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

      1. unpow1 82.0%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in b around inf 55.7%

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

   8. Taylor expanded in j around inf 53.6%

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

      1. cancel-sign-sub-inv 53.6%

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

      2. associate-/l* 53.6%

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

      3. metadata-eval 53.6%

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

      4. *-commutative 53.6%

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

   10. Simplified 53.6%

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

   11. Taylor expanded in j around 0 40.3%

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

   if -2.45e151 < b < -8.20000000000000001e-94

   1. Initial program 90.1%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in j around inf 28.7%

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

   if -8.20000000000000001e-94 < b < -6.79999999999999966e-238

   1. Initial program 86.2%

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

      1. pow1 86.2%

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

      2. associate-*l* 88.4%

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

      3. *-commutative 88.4%

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

   4. Applied egg-rr 88.4%

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

      1. unpow1 88.4%

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

      2. associate-*l* 92.6%

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

      3. *-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in y around 0 69.9%

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

      1. distribute-lft-out 69.9%

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

      2. *-commutative 69.9%

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

      3. *-commutative 69.9%

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

   9. Simplified 69.9%

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

   10. Taylor expanded in b around 0 63.4%

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

   11. Taylor expanded in a around inf 23.6%

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

       1. *-commutative 23.6%

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

   13. Simplified 23.6%

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

   if -6.79999999999999966e-238 < b < 7.5999999999999999e-13

   1. Initial program 94.0%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in j around inf 27.5%

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

      1. metadata-eval 27.5%

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

      2. distribute-lft-neg-in 27.5%

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

      3. associate-*r* 27.5%

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

      4. *-commutative 27.5%

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

      5. distribute-rgt-neg-in 27.5%

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

      6. distribute-lft-neg-in 27.5%

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

      7. metadata-eval 27.5%

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

   7. Simplified 27.5%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-94}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-238}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-13}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 78.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{+66}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 2e+66)
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* k (* j 27.0)))
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -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 tmp;
	if (t <= 2e+66) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= 2d+66) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - (k * (j * 27.0d0))
    else
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= 2e+66) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= 2e+66:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0))
	else:
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 2e+66)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= 2e+66)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	else
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 2e+66], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.99999999999999989e66

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. distribute-lft-out 82.7%

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

      2. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   if 1.99999999999999989e66 < t

   1. Initial program 85.1%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 78.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{+66}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+239}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= z -2.32e-63)
   (* t (* (* 18.0 z) (* x y)))
   (if (<= z 6.5e+239)
     (* -4.0 (+ (* x i) (* t a)))
     (* z (* (* x 18.0) (* t y))))))

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 (z <= -2.32e-63) {
		tmp = t * ((18.0 * z) * (x * y));
	} else if (z <= 6.5e+239) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = z * ((x * 18.0) * (t * y));
	}
	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 (z <= (-2.32d-63)) then
        tmp = t * ((18.0d0 * z) * (x * y))
    else if (z <= 6.5d+239) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else
        tmp = z * ((x * 18.0d0) * (t * y))
    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 (z <= -2.32e-63) {
		tmp = t * ((18.0 * z) * (x * y));
	} else if (z <= 6.5e+239) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = z * ((x * 18.0) * (t * y));
	}
	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 z <= -2.32e-63:
		tmp = t * ((18.0 * z) * (x * y))
	elif z <= 6.5e+239:
		tmp = -4.0 * ((x * i) + (t * a))
	else:
		tmp = z * ((x * 18.0) * (t * y))
	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 (z <= -2.32e-63)
		tmp = Float64(t * Float64(Float64(18.0 * z) * Float64(x * y)));
	elseif (z <= 6.5e+239)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	else
		tmp = Float64(z * Float64(Float64(x * 18.0) * Float64(t * y)));
	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 (z <= -2.32e-63)
		tmp = t * ((18.0 * z) * (x * y));
	elseif (z <= 6.5e+239)
		tmp = -4.0 * ((x * i) + (t * a));
	else
		tmp = z * ((x * 18.0) * (t * y));
	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[z, -2.32e-63], N[(t * N[(N[(18.0 * z), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+239], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * 18.0), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3199999999999999e-63

   1. Initial program 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 53.5%

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

      1. pow1 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-*r* 53.2%

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

   7. Applied egg-rr 53.2%

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

      1. unpow1 53.2%

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

      2. associate-*l* 53.2%

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

   9. Simplified 53.2%

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

   10. Taylor expanded in t around inf 36.8%

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

       1. *-commutative 36.8%

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

       2. associate-*r* 36.8%

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

       3. associate-*r* 38.1%

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

       4. associate-*l* 38.2%

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

       5. *-commutative 38.2%

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

   12. Simplified 38.2%

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

   if -2.3199999999999999e-63 < z < 6.5e239

   1. Initial program 88.7%

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

      1. pow1 88.7%

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

      2. associate-*l* 88.0%

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

      3. *-commutative 88.0%

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

   4. Applied egg-rr 88.0%

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

      1. unpow1 88.0%

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

      2. associate-*l* 89.8%

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

      3. *-commutative 89.8%

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

   6. Simplified 89.8%

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

   7. Taylor expanded in y around 0 82.2%

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

      1. distribute-lft-out 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

   9. Simplified 82.2%

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

   10. Taylor expanded in b around 0 65.3%

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

   11. Taylor expanded in j around 0 47.5%

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

   if 6.5e239 < z

   1. Initial program 71.7%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in x around inf 54.2%

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

   6. Taylor expanded in z around inf 53.7%

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

   7. Taylor expanded in i around 0 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*r* 53.7%

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

      3. associate-*l* 53.7%

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

      4. *-commutative 53.7%

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

      5. associate-*l* 53.7%

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

      6. *-commutative 53.7%

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

   9. Simplified 53.7%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.32 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+239}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151} \lor \neg \left(b \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= b -2.45e+151) (not (<= b 1.6e-9))) (* b c) (* k (* j -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.45e+151) || !(b <= 1.6e-9)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.45d+151)) .or. (.not. (b <= 1.6d-9))) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.45e+151) || !(b <= 1.6e-9)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b <= -2.45e+151) or not (b <= 1.6e-9):
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((b <= -2.45e+151) || !(b <= 1.6e-9))
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b <= -2.45e+151) || ~((b <= 1.6e-9)))
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[b, -2.45e+151], N[Not[LessEqual[b, 1.6e-9]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.45e151 or 1.60000000000000006e-9 < b

   1. Initial program 82.0%

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

      1. pow1 82.0%

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

      2. associate-*l* 82.0%

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

      3. *-commutative 82.0%

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

   4. Applied egg-rr 82.0%

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

      1. unpow1 82.0%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in b around inf 55.7%

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

   8. Taylor expanded in j around inf 53.6%

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

      1. cancel-sign-sub-inv 53.6%

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

      2. associate-/l* 53.6%

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

      3. metadata-eval 53.6%

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

      4. *-commutative 53.6%

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

   10. Simplified 53.6%

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

   11. Taylor expanded in j around 0 40.3%

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

   if -2.45e151 < b < 1.60000000000000006e-9

   1. Initial program 90.7%

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

   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. Add Preprocessing

   5. Taylor expanded in j around inf 24.5%

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

      1. metadata-eval 24.5%

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

      2. distribute-lft-neg-in 24.5%

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

      3. associate-*r* 24.5%

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

      4. *-commutative 24.5%

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

      5. distribute-rgt-neg-in 24.5%

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

      6. distribute-lft-neg-in 24.5%

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

      7. metadata-eval 24.5%

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

   7. Simplified 24.5%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151} \lor \neg \left(b \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151} \lor \neg \left(b \leq 1.06 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= b -2.45e+151) (not (<= b 1.06e-9))) (* b c) (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -2.45e+151) || !(b <= 1.06e-9)) {
		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 ((b <= (-2.45d+151)) .or. (.not. (b <= 1.06d-9))) 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 ((b <= -2.45e+151) || !(b <= 1.06e-9)) {
		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 (b <= -2.45e+151) or not (b <= 1.06e-9):
		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 ((b <= -2.45e+151) || !(b <= 1.06e-9))
		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 ((b <= -2.45e+151) || ~((b <= 1.06e-9)))
		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[b, -2.45e+151], N[Not[LessEqual[b, 1.06e-9]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.45e151 or 1.0600000000000001e-9 < b

   1. Initial program 82.0%

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

      1. pow1 82.0%

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

      2. associate-*l* 82.0%

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

      3. *-commutative 82.0%

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

   4. Applied egg-rr 82.0%

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

      1. unpow1 82.0%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in b around inf 55.7%

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

   8. Taylor expanded in j around inf 53.6%

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

      1. cancel-sign-sub-inv 53.6%

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

      2. associate-/l* 53.6%

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

      3. metadata-eval 53.6%

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

      4. *-commutative 53.6%

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

   10. Simplified 53.6%

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

   11. Taylor expanded in j around 0 40.3%

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

   if -2.45e151 < b < 1.0600000000000001e-9

   1. Initial program 90.7%

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

   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. Add Preprocessing

   5. Taylor expanded in j around inf 24.5%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+151} \lor \neg \left(b \leq 1.06 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.1% 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 87.7%

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

   1. pow1 87.7%

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

   2. associate-*l* 87.5%

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

   3. *-commutative 87.5%

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

4. Applied egg-rr 87.5%

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

   1. unpow1 87.5%

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

   2. associate-*l* 87.4%

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

   3. *-commutative 87.4%

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

6. Simplified 87.4%

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

7. Taylor expanded in b around inf 40.5%

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

8. Taylor expanded in j around inf 39.9%

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

   1. cancel-sign-sub-inv 39.9%

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

   2. associate-/l* 40.8%

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

   3. metadata-eval 40.8%

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

   4. *-commutative 40.8%

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

10. Simplified 40.8%

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

11. Taylor expanded in j around 0 20.7%

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

Developer target: 89.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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