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

Percentage Accurate: 86.1% → 92.2%

Time: 17.4s

Alternatives: 15

Speedup: 0.7×

• 49.3% 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: 86.1% 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, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-32} \lor \neg \left(x \leq 6.6 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -8e-32) (not (<= x 6.6e-35)))
   (+
    (*
     x
     (+
      (* -4.0 i)
      (+ (* -4.0 (/ (* a t) x)) (+ (* 18.0 (* t (* y z))) (/ (* b c) x)))))
    (* j (* k -27.0)))
   (-
    (-
     (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
     (* 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 ((x <= -8e-32) || !(x <= 6.6e-35)) {
		tmp = (x * ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))))) + (j * (k * -27.0));
	} else {
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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 ((x <= (-8d-32)) .or. (.not. (x <= 6.6d-35))) then
        tmp = (x * (((-4.0d0) * i) + (((-4.0d0) * ((a * t) / x)) + ((18.0d0 * (t * (y * z))) + ((b * c) / x))))) + (j * (k * (-27.0d0)))
    else
        tmp = (((b * c) + ((t * (z * (y * (x * 18.0d0)))) - (t * (a * 4.0d0)))) - (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 ((x <= -8e-32) || !(x <= 6.6e-35)) {
		tmp = (x * ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))))) + (j * (k * -27.0));
	} else {
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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 (x <= -8e-32) or not (x <= 6.6e-35):
		tmp = (x * ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))))) + (j * (k * -27.0))
	else:
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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 ((x <= -8e-32) || !(x <= 6.6e-35))
		tmp = Float64(Float64(x * Float64(Float64(-4.0 * i) + Float64(Float64(-4.0 * Float64(Float64(a * t) / x)) + Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(Float64(b * c) / x))))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	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 <= -8e-32) || ~((x <= 6.6e-35)))
		tmp = (x * ((-4.0 * i) + ((-4.0 * ((a * t) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))))) + (j * (k * -27.0));
	else
		tmp = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (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[x, -8e-32], N[Not[LessEqual[x, 6.6e-35]], $MachinePrecision]], N[(N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000045e-32 or 6.6000000000000001e-35 < x

   1. Initial program 67.6%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in x around inf 89.1%

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

   if -8.00000000000000045e-32 < x < 6.6000000000000001e-35

   1. Initial program 97.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-32} \lor \neg \left(x \leq 6.6 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.7% accurate, 0.5× speedup

Math

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

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

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

Java

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0))) <= Inf)
		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(j * Float64(k * -27.0)) + Float64(z * Float64(Float64(18.0 * Float64(t * Float64(x * y))) + Float64(Float64(b * c) / z))));
	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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0))) <= Inf)
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = (j * (k * -27.0)) + (z * ((18.0 * (t * (x * y))) + ((b * c) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

   3. Simplified 93.9%

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

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

   1. Initial program 0.0%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in z around inf 16.1%

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

   7. Taylor expanded in b around inf 58.1%

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

4. Final simplification 89.6%

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

Alternative 3: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ t_3 := t\_1 + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+59}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+127}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* j (* k -27.0)))
        (t_2 (+ t_1 (+ (* b c) (* -4.0 (* x i)))))
        (t_3 (+ t_1 (* t (+ (* -4.0 a) (* 18.0 (* x (* y z))))))))
   (if (<= t -2.5e+162)
     t_3
     (if (<= t -1.7e+128)
       t_2
       (if (<= t -8.2e+59)
         t_3
         (if (<= t -1.75e+43)
           t_2
           (if (<= t -3.8e-70)
             t_3
             (if (<= t 1.16e-58)
               t_2
               (if (<= t 1.82e+127)
                 (+ t_1 (+ (* b c) (* -4.0 (* a t))))
                 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 = j * (k * -27.0);
	double t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	double t_3 = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -2.5e+162) {
		tmp = t_3;
	} else if (t <= -1.7e+128) {
		tmp = t_2;
	} else if (t <= -8.2e+59) {
		tmp = t_3;
	} else if (t <= -1.75e+43) {
		tmp = t_2;
	} else if (t <= -3.8e-70) {
		tmp = t_3;
	} else if (t <= 1.16e-58) {
		tmp = t_2;
	} else if (t <= 1.82e+127) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} 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 = j * (k * (-27.0d0))
    t_2 = t_1 + ((b * c) + ((-4.0d0) * (x * i)))
    t_3 = t_1 + (t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z)))))
    if (t <= (-2.5d+162)) then
        tmp = t_3
    else if (t <= (-1.7d+128)) then
        tmp = t_2
    else if (t <= (-8.2d+59)) then
        tmp = t_3
    else if (t <= (-1.75d+43)) then
        tmp = t_2
    else if (t <= (-3.8d-70)) then
        tmp = t_3
    else if (t <= 1.16d-58) then
        tmp = t_2
    else if (t <= 1.82d+127) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (a * t)))
    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 = j * (k * -27.0);
	double t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	double t_3 = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -2.5e+162) {
		tmp = t_3;
	} else if (t <= -1.7e+128) {
		tmp = t_2;
	} else if (t <= -8.2e+59) {
		tmp = t_3;
	} else if (t <= -1.75e+43) {
		tmp = t_2;
	} else if (t <= -3.8e-70) {
		tmp = t_3;
	} else if (t <= 1.16e-58) {
		tmp = t_2;
	} else if (t <= 1.82e+127) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} 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 = j * (k * -27.0)
	t_2 = t_1 + ((b * c) + (-4.0 * (x * i)))
	t_3 = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))))
	tmp = 0
	if t <= -2.5e+162:
		tmp = t_3
	elif t <= -1.7e+128:
		tmp = t_2
	elif t <= -8.2e+59:
		tmp = t_3
	elif t <= -1.75e+43:
		tmp = t_2
	elif t <= -3.8e-70:
		tmp = t_3
	elif t <= 1.16e-58:
		tmp = t_2
	elif t <= 1.82e+127:
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)))
	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(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))))
	t_3 = Float64(t_1 + Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z))))))
	tmp = 0.0
	if (t <= -2.5e+162)
		tmp = t_3;
	elseif (t <= -1.7e+128)
		tmp = t_2;
	elseif (t <= -8.2e+59)
		tmp = t_3;
	elseif (t <= -1.75e+43)
		tmp = t_2;
	elseif (t <= -3.8e-70)
		tmp = t_3;
	elseif (t <= 1.16e-58)
		tmp = t_2;
	elseif (t <= 1.82e+127)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))));
	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 = j * (k * -27.0);
	t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	t_3 = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	tmp = 0.0;
	if (t <= -2.5e+162)
		tmp = t_3;
	elseif (t <= -1.7e+128)
		tmp = t_2;
	elseif (t <= -8.2e+59)
		tmp = t_3;
	elseif (t <= -1.75e+43)
		tmp = t_2;
	elseif (t <= -3.8e-70)
		tmp = t_3;
	elseif (t <= 1.16e-58)
		tmp = t_2;
	elseif (t <= 1.82e+127)
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+162], t$95$3, If[LessEqual[t, -1.7e+128], t$95$2, If[LessEqual[t, -8.2e+59], t$95$3, If[LessEqual[t, -1.75e+43], t$95$2, If[LessEqual[t, -3.8e-70], t$95$3, If[LessEqual[t, 1.16e-58], t$95$2, If[LessEqual[t, 1.82e+127], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999998e162 or -1.6999999999999999e128 < t < -8.2e59 or -1.7500000000000001e43 < t < -3.7999999999999998e-70 or 1.82000000000000009e127 < t

   1. Initial program 82.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around inf 85.3%

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

   if -2.4999999999999998e162 < t < -1.6999999999999999e128 or -8.2e59 < t < -1.7500000000000001e43 or -3.7999999999999998e-70 < t < 1.16000000000000007e-58

   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 83.8%

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

   5. Taylor expanded in t around 0 84.7%

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

   if 1.16000000000000007e-58 < t < 1.82000000000000009e127

   1. Initial program 80.3%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in x around 0 80.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+128}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-63}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;t\_1 + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -2.2e+186)
     t_2
     (if (<= (* b c) -1.25e-63)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 2.3e-42)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 1.7e+108)
           (+ t_1 (* x (* (* t y) (* 18.0 z))))
           t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+186) {
		tmp = t_2;
	} else if ((b * c) <= -1.25e-63) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 2.3e-42) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 1.7e+108) {
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-2.2d+186)) then
        tmp = t_2
    else if ((b * c) <= (-1.25d-63)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 2.3d-42) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 1.7d+108) then
        tmp = t_1 + (x * ((t * y) * (18.0d0 * z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+186) {
		tmp = t_2;
	} else if ((b * c) <= -1.25e-63) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 2.3e-42) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 1.7e+108) {
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -2.2e+186:
		tmp = t_2
	elif (b * c) <= -1.25e-63:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 2.3e-42:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 1.7e+108:
		tmp = t_1 + (x * ((t * y) * (18.0 * z)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+186)
		tmp = t_2;
	elseif (Float64(b * c) <= -1.25e-63)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 2.3e-42)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 1.7e+108)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(t * y) * Float64(18.0 * z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -2.2e+186)
		tmp = t_2;
	elseif ((b * c) <= -1.25e-63)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 2.3e-42)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 1.7e+108)
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+186], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e-63], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.3e-42], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.7e+108], N[(t$95$1 + N[(x * N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.1999999999999998e186 or 1.69999999999999998e108 < (*.f64 b c)

   1. Initial program 72.0%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in b around inf 76.8%

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

   if -2.1999999999999998e186 < (*.f64 b c) < -1.25e-63

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -1.25e-63 < (*.f64 b c) < 2.30000000000000004e-42

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

   if 2.30000000000000004e-42 < (*.f64 b c) < 1.69999999999999998e108

   1. Initial program 76.3%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*r* 69.7%

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

      3. associate-*l* 69.7%

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

      4. *-commutative 69.7%

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

      5. *-commutative 69.7%

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

      6. associate-*r* 72.9%

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

      7. associate-*l* 73.0%

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

      8. *-commutative 73.0%

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

   7. Simplified 73.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-64}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+170}:\\ \;\;\;\;t\_1 + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -3.2e+188)
     t_2
     (if (<= (* b c) -7.8e-64)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 1.4e-43)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 4.2e+170)
           (+ t_1 (* x (* t (* z (* 18.0 y)))))
           t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -3.2e+188) {
		tmp = t_2;
	} else if ((b * c) <= -7.8e-64) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.4e-43) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 4.2e+170) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-3.2d+188)) then
        tmp = t_2
    else if ((b * c) <= (-7.8d-64)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 1.4d-43) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 4.2d+170) then
        tmp = t_1 + (x * (t * (z * (18.0d0 * y))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -3.2e+188) {
		tmp = t_2;
	} else if ((b * c) <= -7.8e-64) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.4e-43) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 4.2e+170) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -3.2e+188:
		tmp = t_2
	elif (b * c) <= -7.8e-64:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 1.4e-43:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 4.2e+170:
		tmp = t_1 + (x * (t * (z * (18.0 * y))))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -3.2e+188)
		tmp = t_2;
	elseif (Float64(b * c) <= -7.8e-64)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 1.4e-43)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 4.2e+170)
		tmp = Float64(t_1 + Float64(x * Float64(t * Float64(z * Float64(18.0 * y)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -3.2e+188)
		tmp = t_2;
	elseif ((b * c) <= -7.8e-64)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 1.4e-43)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 4.2e+170)
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.2e+188], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -7.8e-64], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.4e-43], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+170], N[(t$95$1 + N[(x * N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.1999999999999997e188 or 4.19999999999999996e170 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -3.1999999999999997e188 < (*.f64 b c) < -7.7999999999999994e-64

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -7.7999999999999994e-64 < (*.f64 b c) < 1.3999999999999999e-43

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

   if 1.3999999999999999e-43 < (*.f64 b c) < 4.19999999999999996e170

   1. Initial program 78.7%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-*r* 65.5%

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

      3. associate-*l* 65.5%

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

      4. *-commutative 65.5%

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

      5. *-commutative 65.5%

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

      6. associate-*l* 65.5%

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

      7. *-commutative 65.5%

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

      8. associate-*l* 65.6%

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

      9. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+188}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-64}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+170}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+184}:\\ \;\;\;\;t\_1 + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -2.2e+190)
     t_2
     (if (<= (* b c) -2.6e-65)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 1.05e-41)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 1.25e+184)
           (+ t_1 (* x (* 18.0 (* t (* y z)))))
           t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+190) {
		tmp = t_2;
	} else if ((b * c) <= -2.6e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.05e-41) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 1.25e+184) {
		tmp = t_1 + (x * (18.0 * (t * (y * z))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-2.2d+190)) then
        tmp = t_2
    else if ((b * c) <= (-2.6d-65)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 1.05d-41) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 1.25d+184) then
        tmp = t_1 + (x * (18.0d0 * (t * (y * z))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+190) {
		tmp = t_2;
	} else if ((b * c) <= -2.6e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.05e-41) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 1.25e+184) {
		tmp = t_1 + (x * (18.0 * (t * (y * z))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -2.2e+190:
		tmp = t_2
	elif (b * c) <= -2.6e-65:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 1.05e-41:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 1.25e+184:
		tmp = t_1 + (x * (18.0 * (t * (y * z))))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+190)
		tmp = t_2;
	elseif (Float64(b * c) <= -2.6e-65)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 1.05e-41)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 1.25e+184)
		tmp = Float64(t_1 + Float64(x * Float64(18.0 * Float64(t * Float64(y * z)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -2.2e+190)
		tmp = t_2;
	elseif ((b * c) <= -2.6e-65)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 1.05e-41)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 1.25e+184)
		tmp = t_1 + (x * (18.0 * (t * (y * z))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+190], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -2.6e-65], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-41], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.25e+184], N[(t$95$1 + N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.2e190 or 1.25e184 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -2.2e190 < (*.f64 b c) < -2.6000000000000001e-65

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -2.6000000000000001e-65 < (*.f64 b c) < 1.05000000000000006e-41

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

   if 1.05000000000000006e-41 < (*.f64 b c) < 1.25e184

   1. Initial program 78.7%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-*r* 65.5%

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

      3. associate-*l* 65.5%

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

      4. *-commutative 65.5%

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

      5. *-commutative 65.5%

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

      6. associate-*r* 68.1%

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

      7. associate-*l* 68.1%

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

      8. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around 0 65.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+190}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-65}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{+181}:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -2.2e+186)
     t_2
     (if (<= (* b c) -3.6e-65)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 8.8e-44)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 6.6e+181)
           (+ t_1 (* 18.0 (* (* y z) (* x t))))
           t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+186) {
		tmp = t_2;
	} else if ((b * c) <= -3.6e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 8.8e-44) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 6.6e+181) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-2.2d+186)) then
        tmp = t_2
    else if ((b * c) <= (-3.6d-65)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 8.8d-44) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 6.6d+181) then
        tmp = t_1 + (18.0d0 * ((y * z) * (x * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.2e+186) {
		tmp = t_2;
	} else if ((b * c) <= -3.6e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 8.8e-44) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 6.6e+181) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -2.2e+186:
		tmp = t_2
	elif (b * c) <= -3.6e-65:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 8.8e-44:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 6.6e+181:
		tmp = t_1 + (18.0 * ((y * z) * (x * t)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+186)
		tmp = t_2;
	elseif (Float64(b * c) <= -3.6e-65)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 8.8e-44)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 6.6e+181)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -2.2e+186)
		tmp = t_2;
	elseif ((b * c) <= -3.6e-65)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 8.8e-44)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 6.6e+181)
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+186], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-65], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.8e-44], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.6e+181], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.1999999999999998e186 or 6.60000000000000034e181 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -2.1999999999999998e186 < (*.f64 b c) < -3.5999999999999998e-65

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -3.5999999999999998e-65 < (*.f64 b c) < 8.80000000000000048e-44

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

   if 8.80000000000000048e-44 < (*.f64 b c) < 6.60000000000000034e181

   1. Initial program 78.7%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around inf 63.0%

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

      1. associate-*r* 63.0%

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

   7. Simplified 63.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+179}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= (* b c) -2.9e+193)
     t_2
     (if (<= (* b c) -7.2e-65)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 1.6e-43)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 7.5e+179)
           (+ t_1 (* 18.0 (* t (* x (* y z)))))
           t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.9e+193) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.6e-43) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 7.5e+179) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if ((b * c) <= (-2.9d+193)) then
        tmp = t_2
    else if ((b * c) <= (-7.2d-65)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 1.6d-43) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 7.5d+179) then
        tmp = t_1 + (18.0d0 * (t * (x * (y * z))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if ((b * c) <= -2.9e+193) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e-65) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 1.6e-43) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 7.5e+179) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if (b * c) <= -2.9e+193:
		tmp = t_2
	elif (b * c) <= -7.2e-65:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 1.6e-43:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 7.5e+179:
		tmp = t_1 + (18.0 * (t * (x * (y * z))))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (Float64(b * c) <= -2.9e+193)
		tmp = t_2;
	elseif (Float64(b * c) <= -7.2e-65)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 1.6e-43)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 7.5e+179)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if ((b * c) <= -2.9e+193)
		tmp = t_2;
	elseif ((b * c) <= -7.2e-65)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 1.6e-43)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 7.5e+179)
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e+193], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-65], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-43], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e+179], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.90000000000000013e193 or 7.50000000000000007e179 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -2.90000000000000013e193 < (*.f64 b c) < -7.1999999999999996e-65

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -7.1999999999999996e-65 < (*.f64 b c) < 1.59999999999999992e-43

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

   if 1.59999999999999992e-43 < (*.f64 b c) < 7.50000000000000007e179

   1. Initial program 78.7%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around inf 63.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+193}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+179}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{-63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+173}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (+ t_1 (* t (* -4.0 a)))))
   (if (<= (* b c) -4.1e+186)
     t_2
     (if (<= (* b c) -3e-63)
       t_3
       (if (<= (* b c) 5.2e-45)
         (+ (* x (* -4.0 i)) (* -27.0 (* j k)))
         (if (<= (* b c) 2.6e+173) t_3 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (t * (-4.0 * a));
	double tmp;
	if ((b * c) <= -4.1e+186) {
		tmp = t_2;
	} else if ((b * c) <= -3e-63) {
		tmp = t_3;
	} else if ((b * c) <= 5.2e-45) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 2.6e+173) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t_1 + (t * ((-4.0d0) * a))
    if ((b * c) <= (-4.1d+186)) then
        tmp = t_2
    else if ((b * c) <= (-3d-63)) then
        tmp = t_3
    else if ((b * c) <= 5.2d-45) then
        tmp = (x * ((-4.0d0) * i)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 2.6d+173) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (t * (-4.0 * a));
	double tmp;
	if ((b * c) <= -4.1e+186) {
		tmp = t_2;
	} else if ((b * c) <= -3e-63) {
		tmp = t_3;
	} else if ((b * c) <= 5.2e-45) {
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	} else if ((b * c) <= 2.6e+173) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t_1 + (t * (-4.0 * a))
	tmp = 0
	if (b * c) <= -4.1e+186:
		tmp = t_2
	elif (b * c) <= -3e-63:
		tmp = t_3
	elif (b * c) <= 5.2e-45:
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k))
	elif (b * c) <= 2.6e+173:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t_1 + Float64(t * Float64(-4.0 * a)))
	tmp = 0.0
	if (Float64(b * c) <= -4.1e+186)
		tmp = t_2;
	elseif (Float64(b * c) <= -3e-63)
		tmp = t_3;
	elseif (Float64(b * c) <= 5.2e-45)
		tmp = Float64(Float64(x * Float64(-4.0 * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 2.6e+173)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t_1 + (t * (-4.0 * a));
	tmp = 0.0;
	if ((b * c) <= -4.1e+186)
		tmp = t_2;
	elseif ((b * c) <= -3e-63)
		tmp = t_3;
	elseif ((b * c) <= 5.2e-45)
		tmp = (x * (-4.0 * i)) + (-27.0 * (j * k));
	elseif ((b * c) <= 2.6e+173)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.1e+186], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -3e-63], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 5.2e-45], N[(N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.6e+173], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.1e186 or 2.5999999999999999e173 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -4.1e186 < (*.f64 b c) < -2.99999999999999979e-63 or 5.19999999999999973e-45 < (*.f64 b c) < 2.5999999999999999e173

   1. Initial program 83.7%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-*r* 56.9%

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

      4. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   if -2.99999999999999979e-63 < (*.f64 b c) < 5.19999999999999973e-45

   1. Initial program 85.9%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in j around 0 63.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-27}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-58}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= t -5e-27)
     (+ t_1 (* x (+ (* -4.0 i) (* 18.0 (* t (* y z))))))
     (if (<= t 2.9e-58)
       (+ t_1 (+ (* b c) (* -4.0 (* x i))))
       (if (<= t 1.25e+127)
         (+ t_1 (+ (* b c) (* -4.0 (* a t))))
         (+ t_1 (* t (+ (* -4.0 a) (* 18.0 (* x (* y z)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -5e-27) {
		tmp = t_1 + (x * ((-4.0 * i) + (18.0 * (t * (y * z)))));
	} else if (t <= 2.9e-58) {
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	} else if (t <= 1.25e+127) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else {
		tmp = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (t <= (-5d-27)) then
        tmp = t_1 + (x * (((-4.0d0) * i) + (18.0d0 * (t * (y * z)))))
    else if (t <= 2.9d-58) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (x * i)))
    else if (t <= 1.25d+127) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (a * t)))
    else
        tmp = t_1 + (t * (((-4.0d0) * a) + (18.0d0 * (x * (y * z)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -5e-27) {
		tmp = t_1 + (x * ((-4.0 * i) + (18.0 * (t * (y * z)))));
	} else if (t <= 2.9e-58) {
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	} else if (t <= 1.25e+127) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else {
		tmp = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if t <= -5e-27:
		tmp = t_1 + (x * ((-4.0 * i) + (18.0 * (t * (y * z)))))
	elif t <= 2.9e-58:
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)))
	elif t <= 1.25e+127:
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)))
	else:
		tmp = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -5e-27)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(t * Float64(y * z))))));
	elseif (t <= 2.9e-58)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))));
	elseif (t <= 1.25e+127)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))));
	else
		tmp = Float64(t_1 + Float64(t * Float64(Float64(-4.0 * a) + Float64(18.0 * Float64(x * Float64(y * z))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -5e-27)
		tmp = t_1 + (x * ((-4.0 * i) + (18.0 * (t * (y * z)))));
	elseif (t <= 2.9e-58)
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	elseif (t <= 1.25e+127)
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	else
		tmp = t_1 + (t * ((-4.0 * a) + (18.0 * (x * (y * z)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-27], N[(t$95$1 + N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-58], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+127], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.0000000000000002e-27

   1. Initial program 86.7%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf 75.4%

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

   if -5.0000000000000002e-27 < t < 2.8999999999999999e-58

   1. Initial program 81.0%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in t around 0 82.0%

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

   if 2.8999999999999999e-58 < t < 1.2500000000000001e127

   1. Initial program 80.3%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in x around 0 80.2%

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

   if 1.2500000000000001e127 < t

   1. Initial program 74.9%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in t around inf 87.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{-23}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i + \frac{b \cdot c}{x}\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-96}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+249}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -1.04e-23)
     (+ t_1 (* x (+ (* -4.0 i) (/ (* b c) x))))
     (if (<= x 2.75e-96)
       (+ t_1 (+ (* b c) (* -4.0 (* a t))))
       (if (<= x 1.3e+249)
         (+ t_1 (+ (* b c) (* -4.0 (* x i))))
         (+ t_1 (* (* t 18.0) (* z (* x 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 t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -1.04e-23) {
		tmp = t_1 + (x * ((-4.0 * i) + ((b * c) / x)));
	} else if (x <= 2.75e-96) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else if (x <= 1.3e+249) {
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	} else {
		tmp = t_1 + ((t * 18.0) * (z * (x * 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) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-1.04d-23)) then
        tmp = t_1 + (x * (((-4.0d0) * i) + ((b * c) / x)))
    else if (x <= 2.75d-96) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (a * t)))
    else if (x <= 1.3d+249) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (x * i)))
    else
        tmp = t_1 + ((t * 18.0d0) * (z * (x * 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 t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -1.04e-23) {
		tmp = t_1 + (x * ((-4.0 * i) + ((b * c) / x)));
	} else if (x <= 2.75e-96) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else if (x <= 1.3e+249) {
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	} else {
		tmp = t_1 + ((t * 18.0) * (z * (x * 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):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -1.04e-23:
		tmp = t_1 + (x * ((-4.0 * i) + ((b * c) / x)))
	elif x <= 2.75e-96:
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)))
	elif x <= 1.3e+249:
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)))
	else:
		tmp = t_1 + ((t * 18.0) * (z * (x * 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)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -1.04e-23)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(-4.0 * i) + Float64(Float64(b * c) / x))));
	elseif (x <= 2.75e-96)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))));
	elseif (x <= 1.3e+249)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))));
	else
		tmp = Float64(t_1 + Float64(Float64(t * 18.0) * Float64(z * Float64(x * 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)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -1.04e-23)
		tmp = t_1 + (x * ((-4.0 * i) + ((b * c) / x)));
	elseif (x <= 2.75e-96)
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	elseif (x <= 1.3e+249)
		tmp = t_1 + ((b * c) + (-4.0 * (x * i)));
	else
		tmp = t_1 + ((t * 18.0) * (z * (x * 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_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.04e-23], N[(t$95$1 + N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-96], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+249], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.04e-23

   1. Initial program 68.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around inf 90.0%

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

   6. Taylor expanded in t around 0 65.5%

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

   if -1.04e-23 < x < 2.7499999999999998e-96

   1. Initial program 99.9%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around 0 85.8%

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

   if 2.7499999999999998e-96 < x < 1.3000000000000001e249

   1. Initial program 74.4%

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

   3. Simplified 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 t around 0 69.6%

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

   if 1.3000000000000001e249 < x

   1. Initial program 40.5%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in x around inf 93.2%

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

   6. Taylor expanded in y around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. associate-*r* 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + \frac{b \cdot c}{x}\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+249}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+249}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (+ (* b c) (* -4.0 (* x i))))))
   (if (<= x -6.2e-80)
     t_2
     (if (<= x 1.3e-99)
       (+ t_1 (+ (* b c) (* -4.0 (* a t))))
       (if (<= x 1.3e+249) t_2 (+ t_1 (* (* t 18.0) (* z (* x 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	double tmp;
	if (x <= -6.2e-80) {
		tmp = t_2;
	} else if (x <= 1.3e-99) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else if (x <= 1.3e+249) {
		tmp = t_2;
	} else {
		tmp = t_1 + ((t * 18.0) * (z * (x * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((b * c) + ((-4.0d0) * (x * i)))
    if (x <= (-6.2d-80)) then
        tmp = t_2
    else if (x <= 1.3d-99) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (a * t)))
    else if (x <= 1.3d+249) then
        tmp = t_2
    else
        tmp = t_1 + ((t * 18.0d0) * (z * (x * 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	double tmp;
	if (x <= -6.2e-80) {
		tmp = t_2;
	} else if (x <= 1.3e-99) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else if (x <= 1.3e+249) {
		tmp = t_2;
	} else {
		tmp = t_1 + ((t * 18.0) * (z * (x * 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):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + ((b * c) + (-4.0 * (x * i)))
	tmp = 0
	if x <= -6.2e-80:
		tmp = t_2
	elif x <= 1.3e-99:
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)))
	elif x <= 1.3e+249:
		tmp = t_2
	else:
		tmp = t_1 + ((t * 18.0) * (z * (x * 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)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i))))
	tmp = 0.0
	if (x <= -6.2e-80)
		tmp = t_2;
	elseif (x <= 1.3e-99)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))));
	elseif (x <= 1.3e+249)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(Float64(t * 18.0) * Float64(z * Float64(x * 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)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + ((b * c) + (-4.0 * (x * i)));
	tmp = 0.0;
	if (x <= -6.2e-80)
		tmp = t_2;
	elseif (x <= 1.3e-99)
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	elseif (x <= 1.3e+249)
		tmp = t_2;
	else
		tmp = t_1 + ((t * 18.0) * (z * (x * 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_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e-80], t$95$2, If[LessEqual[x, 1.3e-99], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+249], t$95$2, N[(t$95$1 + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000032e-80 or 1.30000000000000003e-99 < x < 1.3000000000000001e249

   1. Initial program 73.8%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in t around 0 66.9%

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

   if -6.20000000000000032e-80 < x < 1.30000000000000003e-99

   1. Initial program 99.9%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around 0 87.7%

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

   if 1.3000000000000001e249 < x

   1. Initial program 40.5%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in x around inf 93.2%

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

   6. Taylor expanded in y around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. associate-*r* 74.2%

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

   8. Simplified 74.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+249}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+187} \lor \neg \left(b \cdot c \leq 1.7 \cdot 10^{+171}\right):\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (or (<= (* b c) -2.7e+187) (not (<= (* b c) 1.7e+171)))
     (+ (* b c) t_1)
     (+ t_1 (* t (* -4.0 a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (((b * c) <= -2.7e+187) || !((b * c) <= 1.7e+171)) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_1 + (t * (-4.0 * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (((b * c) <= (-2.7d+187)) .or. (.not. ((b * c) <= 1.7d+171))) then
        tmp = (b * c) + t_1
    else
        tmp = t_1 + (t * ((-4.0d0) * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (((b * c) <= -2.7e+187) || !((b * c) <= 1.7e+171)) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_1 + (t * (-4.0 * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if ((b * c) <= -2.7e+187) or not ((b * c) <= 1.7e+171):
		tmp = (b * c) + t_1
	else:
		tmp = t_1 + (t * (-4.0 * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if ((Float64(b * c) <= -2.7e+187) || !(Float64(b * c) <= 1.7e+171))
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (((b * c) <= -2.7e+187) || ~(((b * c) <= 1.7e+171)))
		tmp = (b * c) + t_1;
	else
		tmp = t_1 + (t * (-4.0 * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.7e+187], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.7e+171]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.70000000000000008e187 or 1.7000000000000001e171 < (*.f64 b c)

   1. Initial program 69.9%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around inf 80.4%

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

   if -2.70000000000000008e187 < (*.f64 b c) < 1.7000000000000001e171

   1. Initial program 84.9%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in a around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*r* 55.7%

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

      4. *-commutative 55.7%

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

   7. Simplified 55.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+187} \lor \neg \left(b \cdot c \leq 1.7 \cdot 10^{+171}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(x \cdot y\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+178}:\\ \;\;\;\;t\_1 + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= z -1.15e-20)
     (+ t_1 (* 18.0 (* (* x y) (* t z))))
     (if (<= z 1.5e+178)
       (+ t_1 (+ (* b c) (* -4.0 (* a t))))
       (+ t_1 (* x (* (* t y) (* 18.0 z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (z <= -1.15e-20) {
		tmp = t_1 + (18.0 * ((x * y) * (t * z)));
	} else if (z <= 1.5e+178) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else {
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (z <= (-1.15d-20)) then
        tmp = t_1 + (18.0d0 * ((x * y) * (t * z)))
    else if (z <= 1.5d+178) then
        tmp = t_1 + ((b * c) + ((-4.0d0) * (a * t)))
    else
        tmp = t_1 + (x * ((t * y) * (18.0d0 * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (z <= -1.15e-20) {
		tmp = t_1 + (18.0 * ((x * y) * (t * z)));
	} else if (z <= 1.5e+178) {
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	} else {
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if z <= -1.15e-20:
		tmp = t_1 + (18.0 * ((x * y) * (t * z)))
	elif z <= 1.5e+178:
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)))
	else:
		tmp = t_1 + (x * ((t * y) * (18.0 * z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (z <= -1.15e-20)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(x * y) * Float64(t * z))));
	elseif (z <= 1.5e+178)
		tmp = Float64(t_1 + Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t))));
	else
		tmp = Float64(t_1 + Float64(x * Float64(Float64(t * y) * Float64(18.0 * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (z <= -1.15e-20)
		tmp = t_1 + (18.0 * ((x * y) * (t * z)));
	elseif (z <= 1.5e+178)
		tmp = t_1 + ((b * c) + (-4.0 * (a * t)));
	else
		tmp = t_1 + (x * ((t * y) * (18.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-20], N[(t$95$1 + N[(18.0 * N[(N[(x * y), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+178], N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-20

   1. Initial program 76.6%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in x around inf 71.8%

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

   6. Taylor expanded in y around inf 58.3%

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

      1. associate-*r* 58.2%

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

      2. associate-*r* 61.8%

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

   8. Simplified 61.8%

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

   9. Taylor expanded in t around 0 58.3%

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

       1. *-commutative 58.3%

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

       2. associate-*r* 61.8%

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

       3. associate-*l* 61.6%

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

   11. Simplified 61.6%

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

   if -1.15e-20 < z < 1.50000000000000008e178

   1. Initial program 84.9%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0 68.9%

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

   if 1.50000000000000008e178 < z

   1. Initial program 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*r* 72.0%

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

      3. associate-*l* 72.0%

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

      4. *-commutative 72.0%

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

      5. *-commutative 72.0%

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

      6. associate-*r* 76.4%

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

      7. associate-*l* 76.4%

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

      8. *-commutative 76.4%

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

   7. Simplified 76.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(x \cdot y\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.0% accurate, 3.4× speedup

Math

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

FPCore

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

C

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

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) + (j * (k * (-27.0d0)))
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) + (j * (k * -27.0));
}

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) + (j * (k * -27.0))

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
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) + (j * (k * -27.0));
end

Wolfram

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

Derivation

1. Initial program 81.5%

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

3. Simplified 86.1%

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

5. Taylor expanded in b around inf 47.2%

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

Developer target: 90.1% 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 2024111 
(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)))