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

Percentage Accurate: 85.8% → 91.9%

Time: 28.3s

Alternatives: 22

Speedup: 1.1×

• 50.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% 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: 91.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in x around inf 55.4%

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

4. Final simplification 92.7%

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

Alternative 2: 49.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ t_3 := t_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -2.45 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;b \cdot c \leq -0.00027:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{-285}:\\ \;\;\;\;t_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 6500000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a 4.0))))
        (t_3 (+ t_1 (* (* t a) -4.0))))
   (if (<= (* b c) -2.45e+150)
     (+ (* b c) t_1)
     (if (<= (* b c) -0.00027)
       (* x (* 18.0 (* z (* y t))))
       (if (<= (* b c) -5.8e-98)
         t_2
         (if (<= (* b c) 1.26e-285)
           (+ t_1 (* (* x i) -4.0))
           (if (<= (* b c) 3e-58)
             t_3
             (if (<= (* b c) 6500000000.0)
               (* x (* 18.0 (* y (* z t))))
               (if (<= (* b c) 2.9e+100) t_3 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (a * 4.0));
	double t_3 = t_1 + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2.45e+150) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -0.00027) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= -5.8e-98) {
		tmp = t_2;
	} else if ((b * c) <= 1.26e-285) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if ((b * c) <= 3e-58) {
		tmp = t_3;
	} else if ((b * c) <= 6500000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 2.9e+100) {
		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.
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 * (a * 4.0d0))
    t_3 = t_1 + ((t * a) * (-4.0d0))
    if ((b * c) <= (-2.45d+150)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-0.00027d0)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if ((b * c) <= (-5.8d-98)) then
        tmp = t_2
    else if ((b * c) <= 1.26d-285) then
        tmp = t_1 + ((x * i) * (-4.0d0))
    else if ((b * c) <= 3d-58) then
        tmp = t_3
    else if ((b * c) <= 6500000000.0d0) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if ((b * c) <= 2.9d+100) 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;
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 * (a * 4.0));
	double t_3 = t_1 + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2.45e+150) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -0.00027) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= -5.8e-98) {
		tmp = t_2;
	} else if ((b * c) <= 1.26e-285) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if ((b * c) <= 3e-58) {
		tmp = t_3;
	} else if ((b * c) <= 6500000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 2.9e+100) {
		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])
[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 * (a * 4.0))
	t_3 = t_1 + ((t * a) * -4.0)
	tmp = 0
	if (b * c) <= -2.45e+150:
		tmp = (b * c) + t_1
	elif (b * c) <= -0.00027:
		tmp = x * (18.0 * (z * (y * t)))
	elif (b * c) <= -5.8e-98:
		tmp = t_2
	elif (b * c) <= 1.26e-285:
		tmp = t_1 + ((x * i) * -4.0)
	elif (b * c) <= 3e-58:
		tmp = t_3
	elif (b * c) <= 6500000000.0:
		tmp = x * (18.0 * (y * (z * t)))
	elif (b * c) <= 2.9e+100:
		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])
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) - Float64(t * Float64(a * 4.0)))
	t_3 = Float64(t_1 + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.45e+150)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -0.00027)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (Float64(b * c) <= -5.8e-98)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.26e-285)
		tmp = Float64(t_1 + Float64(Float64(x * i) * -4.0));
	elseif (Float64(b * c) <= 3e-58)
		tmp = t_3;
	elseif (Float64(b * c) <= 6500000000.0)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (Float64(b * c) <= 2.9e+100)
		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])){:}
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 * (a * 4.0));
	t_3 = t_1 + ((t * a) * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.45e+150)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -0.00027)
		tmp = x * (18.0 * (z * (y * t)));
	elseif ((b * c) <= -5.8e-98)
		tmp = t_2;
	elseif ((b * c) <= 1.26e-285)
		tmp = t_1 + ((x * i) * -4.0);
	elseif ((b * c) <= 3e-58)
		tmp = t_3;
	elseif ((b * c) <= 6500000000.0)
		tmp = x * (18.0 * (y * (z * t)));
	elseif ((b * c) <= 2.9e+100)
		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.
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] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.45e+150], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.00027], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.8e-98], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.26e-285], N[(t$95$1 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e-58], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 6500000000.0], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+100], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -2.45000000000000003e150

   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 86.6%

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

   4. Taylor expanded in b around inf 75.7%

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

   if -2.45000000000000003e150 < (*.f64 b c) < -2.70000000000000003e-4

   1. Initial program 85.6%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 60.8%

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

   5. Taylor expanded in t around inf 42.5%

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

      1. associate-*r* 46.1%

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

   7. Simplified 46.1%

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

   if -2.70000000000000003e-4 < (*.f64 b c) < -5.8e-98 or 2.9e100 < (*.f64 b c)

   1. Initial program 88.0%

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

   2. Taylor expanded in y around 0 80.1%

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

   3. Taylor expanded in j around 0 74.5%

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

   4. Taylor expanded in a around inf 67.1%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. *-commutative 67.1%

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

      4. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   if -5.8e-98 < (*.f64 b c) < 1.26e-285

   1. Initial program 92.2%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if 1.26e-285 < (*.f64 b c) < 3.00000000000000008e-58 or 6.5e9 < (*.f64 b c) < 2.9e100

   1. Initial program 91.8%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 58.0%

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

   if 3.00000000000000008e-58 < (*.f64 b c) < 6.5e9

   1. Initial program 77.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.4%

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

   5. Taylor expanded in t around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l* 62.9%

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

   7. Simplified 62.9%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.45 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -0.00027:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6500000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \]

Alternative 3: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+28} \lor \neg \left(t_2 \leq 4 \cdot 10^{+75}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + t_1\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))) (t_2 (* (* j 27.0) k)))
   (if (or (<= t_2 -5e+28) (not (<= t_2 4e+75)))
     (- (- (* b c) (+ (* 4.0 (* t a)) t_1)) t_2)
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e+28) || !(t_2 <= 4e+75)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (j * 27.0d0) * k
    if ((t_2 <= (-5d+28)) .or. (.not. (t_2 <= 4d+75))) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + t_1)) - t_2
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e+28) || !(t_2 <= 4e+75)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (j * 27.0) * k
	tmp = 0
	if (t_2 <= -5e+28) or not (t_2 <= 4e+75):
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_2 <= -5e+28) || !(t_2 <= 4e+75))
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + t_1)) - t_2);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_2 <= -5e+28) || ~((t_2 <= 4e+75)))
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+28], N[Not[LessEqual[t$95$2, 4e+75]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.99999999999999957e28 or 3.99999999999999971e75 < (*.f64 (*.f64 j 27) k)

   1. Initial program 82.9%

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

   2. Taylor expanded in y around 0 81.4%

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

   if -4.99999999999999957e28 < (*.f64 (*.f64 j 27) k) < 3.99999999999999971e75

   1. Initial program 91.5%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in j around 0 89.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+28} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+75}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 4: 35.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -3.4 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.00032:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* 18.0 (* y (* z t))))) (t_2 (* t (* a -4.0))))
   (if (<= (* b c) -3.4e+150)
     (* b c)
     (if (<= (* b c) -0.00032)
       t_1
       (if (<= (* b c) -2.7e-99)
         t_2
         (if (<= (* b c) 4.3e-284)
           (* i (* x -4.0))
           (if (<= (* b c) 1.75e-75)
             t_2
             (if (<= (* b c) 2.9e+18)
               t_1
               (if (<= (* b c) 1.6e+87) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (18.0 * (y * (z * t)));
	double t_2 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -3.4e+150) {
		tmp = b * c;
	} else if ((b * c) <= -0.00032) {
		tmp = t_1;
	} else if ((b * c) <= -2.7e-99) {
		tmp = t_2;
	} else if ((b * c) <= 4.3e-284) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 1.75e-75) {
		tmp = t_2;
	} else if ((b * c) <= 2.9e+18) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+87) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = x * (18.0d0 * (y * (z * t)))
    t_2 = t * (a * (-4.0d0))
    if ((b * c) <= (-3.4d+150)) then
        tmp = b * c
    else if ((b * c) <= (-0.00032d0)) then
        tmp = t_1
    else if ((b * c) <= (-2.7d-99)) then
        tmp = t_2
    else if ((b * c) <= 4.3d-284) then
        tmp = i * (x * (-4.0d0))
    else if ((b * c) <= 1.75d-75) then
        tmp = t_2
    else if ((b * c) <= 2.9d+18) then
        tmp = t_1
    else if ((b * c) <= 1.6d+87) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (18.0 * (y * (z * t)));
	double t_2 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -3.4e+150) {
		tmp = b * c;
	} else if ((b * c) <= -0.00032) {
		tmp = t_1;
	} else if ((b * c) <= -2.7e-99) {
		tmp = t_2;
	} else if ((b * c) <= 4.3e-284) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 1.75e-75) {
		tmp = t_2;
	} else if ((b * c) <= 2.9e+18) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+87) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (18.0 * (y * (z * t)))
	t_2 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -3.4e+150:
		tmp = b * c
	elif (b * c) <= -0.00032:
		tmp = t_1
	elif (b * c) <= -2.7e-99:
		tmp = t_2
	elif (b * c) <= 4.3e-284:
		tmp = i * (x * -4.0)
	elif (b * c) <= 1.75e-75:
		tmp = t_2
	elif (b * c) <= 2.9e+18:
		tmp = t_1
	elif (b * c) <= 1.6e+87:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -3.4e+150)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -0.00032)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.7e-99)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.3e-284)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (Float64(b * c) <= 1.75e-75)
		tmp = t_2;
	elseif (Float64(b * c) <= 2.9e+18)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e+87)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (18.0 * (y * (z * t)));
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -3.4e+150)
		tmp = b * c;
	elseif ((b * c) <= -0.00032)
		tmp = t_1;
	elseif ((b * c) <= -2.7e-99)
		tmp = t_2;
	elseif ((b * c) <= 4.3e-284)
		tmp = i * (x * -4.0);
	elseif ((b * c) <= 1.75e-75)
		tmp = t_2;
	elseif ((b * c) <= 2.9e+18)
		tmp = t_1;
	elseif ((b * c) <= 1.6e+87)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.4e+150], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.00032], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.7e-99], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.3e-284], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.75e-75], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+18], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+87], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.39999999999999983e150 or 1.6e87 < (*.f64 b c)

   1. Initial program 86.9%

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

   3. Simplified 88.1%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 88.1%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 60.1%

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

   if -3.39999999999999983e150 < (*.f64 b c) < -3.20000000000000026e-4 or 1.74999999999999993e-75 < (*.f64 b c) < 2.9e18

   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 91.5%

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

   4. Taylor expanded in x around inf 59.3%

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

   5. Taylor expanded in t around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. associate-*l* 50.2%

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

   7. Simplified 50.2%

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

   if -3.20000000000000026e-4 < (*.f64 b c) < -2.7e-99 or 4.3000000000000003e-284 < (*.f64 b c) < 1.74999999999999993e-75 or 2.9e18 < (*.f64 b c) < 1.6e87

   1. Initial program 92.0%

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

   3. Simplified 90.7%

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

      1. add-cube-cbrt 90.6%

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

      2. pow3 90.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 90.6%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 90.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in a around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-*l* 42.1%

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

   8. Simplified 42.1%

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

   if -2.7e-99 < (*.f64 b c) < 4.3000000000000003e-284

   1. Initial program 92.2%

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

   3. Simplified 89.3%

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

      1. add-cube-cbrt 89.2%

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

      2. pow3 89.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 89.3%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 89.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in x around inf 33.6%

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

      1. *-commutative 33.6%

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

      2. associate-*r* 33.6%

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

      3. *-commutative 33.6%

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

   8. Simplified 33.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.4 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.00032:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-284}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 5: 35.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.00024:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= (* b c) -2e+152)
     (* b c)
     (if (<= (* b c) -0.00024)
       (* x (* 18.0 (* z (* y t))))
       (if (<= (* b c) -3.5e-100)
         t_1
         (if (<= (* b c) 1.9e-283)
           (* i (* x -4.0))
           (if (<= (* b c) 3.8e-71)
             t_1
             (if (<= (* b c) 2.9e+18)
               (* x (* 18.0 (* y (* z t))))
               (if (<= (* b c) 5.2e+86) t_1 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -2e+152) {
		tmp = b * c;
	} else if ((b * c) <= -0.00024) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= -3.5e-100) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e-283) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 3.8e-71) {
		tmp = t_1;
	} else if ((b * c) <= 2.9e+18) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 5.2e+86) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b * c) <= (-2d+152)) then
        tmp = b * c
    else if ((b * c) <= (-0.00024d0)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if ((b * c) <= (-3.5d-100)) then
        tmp = t_1
    else if ((b * c) <= 1.9d-283) then
        tmp = i * (x * (-4.0d0))
    else if ((b * c) <= 3.8d-71) then
        tmp = t_1
    else if ((b * c) <= 2.9d+18) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if ((b * c) <= 5.2d+86) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -2e+152) {
		tmp = b * c;
	} else if ((b * c) <= -0.00024) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= -3.5e-100) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e-283) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 3.8e-71) {
		tmp = t_1;
	} else if ((b * c) <= 2.9e+18) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 5.2e+86) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -2e+152:
		tmp = b * c
	elif (b * c) <= -0.00024:
		tmp = x * (18.0 * (z * (y * t)))
	elif (b * c) <= -3.5e-100:
		tmp = t_1
	elif (b * c) <= 1.9e-283:
		tmp = i * (x * -4.0)
	elif (b * c) <= 3.8e-71:
		tmp = t_1
	elif (b * c) <= 2.9e+18:
		tmp = x * (18.0 * (y * (z * t)))
	elif (b * c) <= 5.2e+86:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+152)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -0.00024)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (Float64(b * c) <= -3.5e-100)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.9e-283)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (Float64(b * c) <= 3.8e-71)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.9e+18)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (Float64(b * c) <= 5.2e+86)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2e+152)
		tmp = b * c;
	elseif ((b * c) <= -0.00024)
		tmp = x * (18.0 * (z * (y * t)));
	elseif ((b * c) <= -3.5e-100)
		tmp = t_1;
	elseif ((b * c) <= 1.9e-283)
		tmp = i * (x * -4.0);
	elseif ((b * c) <= 3.8e-71)
		tmp = t_1;
	elseif ((b * c) <= 2.9e+18)
		tmp = x * (18.0 * (y * (z * t)));
	elseif ((b * c) <= 5.2e+86)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+152], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.00024], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e-100], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.9e-283], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-71], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+18], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.2e+86], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.0000000000000001e152 or 5.1999999999999995e86 < (*.f64 b c)

   1. Initial program 86.9%

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

   3. Simplified 88.1%

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

      1. add-cube-cbrt 88.1%

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

      2. pow3 88.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.1%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 88.1%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 60.1%

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

   if -2.0000000000000001e152 < (*.f64 b c) < -2.40000000000000006e-4

   1. Initial program 85.6%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 60.8%

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

   5. Taylor expanded in t around inf 42.5%

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

      1. associate-*r* 46.1%

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

   7. Simplified 46.1%

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

   if -2.40000000000000006e-4 < (*.f64 b c) < -3.5000000000000001e-100 or 1.9000000000000001e-283 < (*.f64 b c) < 3.79999999999999992e-71 or 2.9e18 < (*.f64 b c) < 5.1999999999999995e86

   1. Initial program 92.0%

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

   3. Simplified 90.7%

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

      1. add-cube-cbrt 90.6%

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

      2. pow3 90.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 90.6%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 90.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in a around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-*l* 42.1%

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

   8. Simplified 42.1%

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

   if -3.5000000000000001e-100 < (*.f64 b c) < 1.9000000000000001e-283

   1. Initial program 92.2%

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

   3. Simplified 89.3%

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

      1. add-cube-cbrt 89.2%

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

      2. pow3 89.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 89.3%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 89.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in x around inf 33.6%

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

      1. *-commutative 33.6%

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

      2. associate-*r* 33.6%

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

      3. *-commutative 33.6%

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

   8. Simplified 33.6%

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

   if 3.79999999999999992e-71 < (*.f64 b c) < 2.9e18

   1. Initial program 72.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 57.0%

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

   5. Taylor expanded in t around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-*l* 51.5%

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

   7. Simplified 51.5%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.00024:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 6: 57.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ t_4 := j \cdot \left(k \cdot -27\right)\\ t_5 := b \cdot c + t_4\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-92}:\\ \;\;\;\;t_4 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-227}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;t_4 + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+165}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* x (* 4.0 i))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_3 (* t (- (* 18.0 (* z (* x y))) (* a 4.0))))
        (t_4 (* j (* k -27.0)))
        (t_5 (+ (* b c) t_4)))
   (if (<= t -5.2e-20)
     t_3
     (if (<= t -5.8e-92)
       (+ t_4 (* (* x i) -4.0))
       (if (<= t -4.8e-98)
         t_2
         (if (<= t -1.8e-227)
           t_5
           (if (<= t 3.3e-178)
             t_1
             (if (<= t 1.3e-90)
               (+ t_4 (* (* t a) -4.0))
               (if (<= t 1.55e+51)
                 t_1
                 (if (<= t 1.25e+130) t_3 (if (<= t 6e+165) t_5 t_2)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	double t_4 = j * (k * -27.0);
	double t_5 = (b * c) + t_4;
	double tmp;
	if (t <= -5.2e-20) {
		tmp = t_3;
	} else if (t <= -5.8e-92) {
		tmp = t_4 + ((x * i) * -4.0);
	} else if (t <= -4.8e-98) {
		tmp = t_2;
	} else if (t <= -1.8e-227) {
		tmp = t_5;
	} else if (t <= 3.3e-178) {
		tmp = t_1;
	} else if (t <= 1.3e-90) {
		tmp = t_4 + ((t * a) * -4.0);
	} else if (t <= 1.55e+51) {
		tmp = t_1;
	} else if (t <= 1.25e+130) {
		tmp = t_3;
	} else if (t <= 6e+165) {
		tmp = t_5;
	} 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.
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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (b * c) - (x * (4.0d0 * i))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_3 = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    t_4 = j * (k * (-27.0d0))
    t_5 = (b * c) + t_4
    if (t <= (-5.2d-20)) then
        tmp = t_3
    else if (t <= (-5.8d-92)) then
        tmp = t_4 + ((x * i) * (-4.0d0))
    else if (t <= (-4.8d-98)) then
        tmp = t_2
    else if (t <= (-1.8d-227)) then
        tmp = t_5
    else if (t <= 3.3d-178) then
        tmp = t_1
    else if (t <= 1.3d-90) then
        tmp = t_4 + ((t * a) * (-4.0d0))
    else if (t <= 1.55d+51) then
        tmp = t_1
    else if (t <= 1.25d+130) then
        tmp = t_3
    else if (t <= 6d+165) then
        tmp = t_5
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	double t_4 = j * (k * -27.0);
	double t_5 = (b * c) + t_4;
	double tmp;
	if (t <= -5.2e-20) {
		tmp = t_3;
	} else if (t <= -5.8e-92) {
		tmp = t_4 + ((x * i) * -4.0);
	} else if (t <= -4.8e-98) {
		tmp = t_2;
	} else if (t <= -1.8e-227) {
		tmp = t_5;
	} else if (t <= 3.3e-178) {
		tmp = t_1;
	} else if (t <= 1.3e-90) {
		tmp = t_4 + ((t * a) * -4.0);
	} else if (t <= 1.55e+51) {
		tmp = t_1;
	} else if (t <= 1.25e+130) {
		tmp = t_3;
	} else if (t <= 6e+165) {
		tmp = t_5;
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (4.0 * i))
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_3 = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	t_4 = j * (k * -27.0)
	t_5 = (b * c) + t_4
	tmp = 0
	if t <= -5.2e-20:
		tmp = t_3
	elif t <= -5.8e-92:
		tmp = t_4 + ((x * i) * -4.0)
	elif t <= -4.8e-98:
		tmp = t_2
	elif t <= -1.8e-227:
		tmp = t_5
	elif t <= 3.3e-178:
		tmp = t_1
	elif t <= 1.3e-90:
		tmp = t_4 + ((t * a) * -4.0)
	elif t <= 1.55e+51:
		tmp = t_1
	elif t <= 1.25e+130:
		tmp = t_3
	elif t <= 6e+165:
		tmp = t_5
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)))
	t_4 = Float64(j * Float64(k * -27.0))
	t_5 = Float64(Float64(b * c) + t_4)
	tmp = 0.0
	if (t <= -5.2e-20)
		tmp = t_3;
	elseif (t <= -5.8e-92)
		tmp = Float64(t_4 + Float64(Float64(x * i) * -4.0));
	elseif (t <= -4.8e-98)
		tmp = t_2;
	elseif (t <= -1.8e-227)
		tmp = t_5;
	elseif (t <= 3.3e-178)
		tmp = t_1;
	elseif (t <= 1.3e-90)
		tmp = Float64(t_4 + Float64(Float64(t * a) * -4.0));
	elseif (t <= 1.55e+51)
		tmp = t_1;
	elseif (t <= 1.25e+130)
		tmp = t_3;
	elseif (t <= 6e+165)
		tmp = t_5;
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (x * (4.0 * i));
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_3 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	t_4 = j * (k * -27.0);
	t_5 = (b * c) + t_4;
	tmp = 0.0;
	if (t <= -5.2e-20)
		tmp = t_3;
	elseif (t <= -5.8e-92)
		tmp = t_4 + ((x * i) * -4.0);
	elseif (t <= -4.8e-98)
		tmp = t_2;
	elseif (t <= -1.8e-227)
		tmp = t_5;
	elseif (t <= 3.3e-178)
		tmp = t_1;
	elseif (t <= 1.3e-90)
		tmp = t_4 + ((t * a) * -4.0);
	elseif (t <= 1.55e+51)
		tmp = t_1;
	elseif (t <= 1.25e+130)
		tmp = t_3;
	elseif (t <= 6e+165)
		tmp = t_5;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * c), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[t, -5.2e-20], t$95$3, If[LessEqual[t, -5.8e-92], N[(t$95$4 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e-98], t$95$2, If[LessEqual[t, -1.8e-227], t$95$5, If[LessEqual[t, 3.3e-178], t$95$1, If[LessEqual[t, 1.3e-90], N[(t$95$4 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+51], t$95$1, If[LessEqual[t, 1.25e+130], t$95$3, If[LessEqual[t, 6e+165], t$95$5, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.1999999999999999e-20 or 1.55000000000000006e51 < t < 1.2499999999999999e130

   1. Initial program 86.8%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in t around inf 69.6%

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

      1. expm1-log1p-u 46.6%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-udef 44.8%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]

   6. Applied egg-rr 44.8%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. expm1-def 46.6%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-log1p 69.6%

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

      3. associate-*r* 73.2%

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

   8. Simplified 73.2%

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

   if -5.1999999999999999e-20 < t < -5.79999999999999969e-92

   1. Initial program 92.1%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in i around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if -5.79999999999999969e-92 < t < -4.8000000000000001e-98 or 5.99999999999999981e165 < t

   1. Initial program 82.7%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in t around inf 72.1%

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

   if -4.8000000000000001e-98 < t < -1.8e-227 or 1.2499999999999999e130 < t < 5.99999999999999981e165

   1. Initial program 77.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in b around inf 82.1%

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

   if -1.8e-227 < t < 3.3000000000000002e-178 or 1.3e-90 < t < 1.55000000000000006e51

   1. Initial program 93.5%

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

   2. Taylor expanded in y around 0 87.5%

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

   3. Taylor expanded in j around 0 69.7%

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

   4. Taylor expanded in a around 0 58.2%

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

      1. associate-*r* 58.2%

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

      2. *-commutative 58.2%

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

   6. Simplified 58.2%

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

   if 3.3000000000000002e-178 < t < 1.3e-90

   1. Initial program 93.9%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around inf 64.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-227}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+165}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 7: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;b \cdot c \leq -0.00082:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1150000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.4 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* t a) -4.0))))
   (if (<= (* b c) -2.2e+150)
     (+ (* b c) t_1)
     (if (<= (* b c) -0.00082)
       (* x (* 18.0 (* z (* y t))))
       (if (<= (* b c) 3.1e-55)
         t_2
         (if (<= (* b c) 1150000000.0)
           (* x (* 18.0 (* y (* z t))))
           (if (<= (* b c) 5.4e+98) t_2 (- (* b c) (* t (* a 4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2.2e+150) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -0.00082) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= 3.1e-55) {
		tmp = t_2;
	} else if ((b * c) <= 1150000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 5.4e+98) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (t * (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 + ((t * a) * (-4.0d0))
    if ((b * c) <= (-2.2d+150)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-0.00082d0)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if ((b * c) <= 3.1d-55) then
        tmp = t_2
    else if ((b * c) <= 1150000000.0d0) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if ((b * c) <= 5.4d+98) then
        tmp = t_2
    else
        tmp = (b * c) - (t * (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2.2e+150) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -0.00082) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= 3.1e-55) {
		tmp = t_2;
	} else if ((b * c) <= 1150000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if ((b * c) <= 5.4e+98) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (t * (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 + ((t * a) * -4.0)
	tmp = 0
	if (b * c) <= -2.2e+150:
		tmp = (b * c) + t_1
	elif (b * c) <= -0.00082:
		tmp = x * (18.0 * (z * (y * t)))
	elif (b * c) <= 3.1e-55:
		tmp = t_2
	elif (b * c) <= 1150000000.0:
		tmp = x * (18.0 * (y * (z * t)))
	elif (b * c) <= 5.4e+98:
		tmp = t_2
	else:
		tmp = (b * c) - (t * (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(t * a) * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+150)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -0.00082)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (Float64(b * c) <= 3.1e-55)
		tmp = t_2;
	elseif (Float64(b * c) <= 1150000000.0)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (Float64(b * c) <= 5.4e+98)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 + ((t * a) * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.2e+150)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -0.00082)
		tmp = x * (18.0 * (z * (y * t)));
	elseif ((b * c) <= 3.1e-55)
		tmp = t_2;
	elseif ((b * c) <= 1150000000.0)
		tmp = x * (18.0 * (y * (z * t)));
	elseif ((b * c) <= 5.4e+98)
		tmp = t_2;
	else
		tmp = (b * c) - (t * (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+150], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.00082], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.1e-55], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1150000000.0], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.4e+98], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.19999999999999999e150

   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 86.6%

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

   4. Taylor expanded in b around inf 75.7%

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

   if -2.19999999999999999e150 < (*.f64 b c) < -8.1999999999999998e-4

   1. Initial program 85.6%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 60.8%

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

   5. Taylor expanded in t around inf 42.5%

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

      1. associate-*r* 46.1%

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

   7. Simplified 46.1%

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

   if -8.1999999999999998e-4 < (*.f64 b c) < 3.09999999999999997e-55 or 1.15e9 < (*.f64 b c) < 5.4e98

   1. Initial program 91.1%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 52.1%

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

   if 3.09999999999999997e-55 < (*.f64 b c) < 1.15e9

   1. Initial program 77.0%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.4%

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

   5. Taylor expanded in t around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l* 62.9%

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

   7. Simplified 62.9%

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

   if 5.4e98 < (*.f64 b c)

   1. Initial program 89.0%

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

   2. Taylor expanded in y around 0 81.5%

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

   3. Taylor expanded in j around 0 79.2%

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

   4. Taylor expanded in a around inf 72.7%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

      3. *-commutative 72.7%

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

      4. *-commutative 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -0.00082:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1150000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.4 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \]

Alternative 8: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := b \cdot c + t_2\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{+39}:\\ \;\;\;\;t_2 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+76} \lor \neg \left(i \leq 2 \cdot 10^{+129}\right) \land i \leq 2.15 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ (* b c) t_2)))
   (if (<= i -9.2e+64)
     (- (* b c) (* x (* 4.0 i)))
     (if (<= i -5.3e+39)
       (+ t_2 (* (* x i) -4.0))
       (if (<= i -9e-68)
         t_1
         (if (<= i -4.7e-113)
           t_3
           (if (<= i 5.5e-181)
             (- (* b c) (* t (* a 4.0)))
             (if (<= i 2.8e-41)
               t_1
               (if (or (<= i 1.35e+76)
                       (and (not (<= i 2e+129)) (<= i 2.15e+153)))
                 t_3
                 (- (* (* t a) (- 4.0)) (* 4.0 (* x i))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) + t_2;
	double tmp;
	if (i <= -9.2e+64) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (i <= -5.3e+39) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if (i <= -9e-68) {
		tmp = t_1;
	} else if (i <= -4.7e-113) {
		tmp = t_3;
	} else if (i <= 5.5e-181) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (i <= 2.8e-41) {
		tmp = t_1;
	} else if ((i <= 1.35e+76) || (!(i <= 2e+129) && (i <= 2.15e+153))) {
		tmp = t_3;
	} else {
		tmp = ((t * a) * -4.0) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = (b * c) + t_2
    if (i <= (-9.2d+64)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (i <= (-5.3d+39)) then
        tmp = t_2 + ((x * i) * (-4.0d0))
    else if (i <= (-9d-68)) then
        tmp = t_1
    else if (i <= (-4.7d-113)) then
        tmp = t_3
    else if (i <= 5.5d-181) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else if (i <= 2.8d-41) then
        tmp = t_1
    else if ((i <= 1.35d+76) .or. (.not. (i <= 2d+129)) .and. (i <= 2.15d+153)) then
        tmp = t_3
    else
        tmp = ((t * a) * -4.0d0) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) + t_2;
	double tmp;
	if (i <= -9.2e+64) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (i <= -5.3e+39) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if (i <= -9e-68) {
		tmp = t_1;
	} else if (i <= -4.7e-113) {
		tmp = t_3;
	} else if (i <= 5.5e-181) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (i <= 2.8e-41) {
		tmp = t_1;
	} else if ((i <= 1.35e+76) || (!(i <= 2e+129) && (i <= 2.15e+153))) {
		tmp = t_3;
	} else {
		tmp = ((t * a) * -4.0) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = j * (k * -27.0)
	t_3 = (b * c) + t_2
	tmp = 0
	if i <= -9.2e+64:
		tmp = (b * c) - (x * (4.0 * i))
	elif i <= -5.3e+39:
		tmp = t_2 + ((x * i) * -4.0)
	elif i <= -9e-68:
		tmp = t_1
	elif i <= -4.7e-113:
		tmp = t_3
	elif i <= 5.5e-181:
		tmp = (b * c) - (t * (a * 4.0))
	elif i <= 2.8e-41:
		tmp = t_1
	elif (i <= 1.35e+76) or (not (i <= 2e+129) and (i <= 2.15e+153)):
		tmp = t_3
	else:
		tmp = ((t * a) * -4.0) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(b * c) + t_2)
	tmp = 0.0
	if (i <= -9.2e+64)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (i <= -5.3e+39)
		tmp = Float64(t_2 + Float64(Float64(x * i) * -4.0));
	elseif (i <= -9e-68)
		tmp = t_1;
	elseif (i <= -4.7e-113)
		tmp = t_3;
	elseif (i <= 5.5e-181)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	elseif (i <= 2.8e-41)
		tmp = t_1;
	elseif ((i <= 1.35e+76) || (!(i <= 2e+129) && (i <= 2.15e+153)))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) * Float64(-4.0)) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_2 = j * (k * -27.0);
	t_3 = (b * c) + t_2;
	tmp = 0.0;
	if (i <= -9.2e+64)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (i <= -5.3e+39)
		tmp = t_2 + ((x * i) * -4.0);
	elseif (i <= -9e-68)
		tmp = t_1;
	elseif (i <= -4.7e-113)
		tmp = t_3;
	elseif (i <= 5.5e-181)
		tmp = (b * c) - (t * (a * 4.0));
	elseif (i <= 2.8e-41)
		tmp = t_1;
	elseif ((i <= 1.35e+76) || (~((i <= 2e+129)) && (i <= 2.15e+153)))
		tmp = t_3;
	else
		tmp = ((t * a) * -4.0) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[i, -9.2e+64], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.3e+39], N[(t$95$2 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e-68], t$95$1, If[LessEqual[i, -4.7e-113], t$95$3, If[LessEqual[i, 5.5e-181], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e-41], t$95$1, If[Or[LessEqual[i, 1.35e+76], And[N[Not[LessEqual[i, 2e+129]], $MachinePrecision], LessEqual[i, 2.15e+153]]], t$95$3, N[(N[(N[(t * a), $MachinePrecision] * (-4.0)), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.2e64

   1. Initial program 91.1%

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

   2. Taylor expanded in y around 0 80.4%

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

   3. Taylor expanded in j around 0 75.2%

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

   4. Taylor expanded in a around 0 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if -9.2e64 < i < -5.29999999999999979e39

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in i around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -5.29999999999999979e39 < i < -8.99999999999999998e-68 or 5.50000000000000033e-181 < i < 2.8000000000000002e-41

   1. Initial program 84.2%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in t around inf 64.9%

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

   if -8.99999999999999998e-68 < i < -4.7000000000000002e-113 or 2.8000000000000002e-41 < i < 1.34999999999999995e76 or 2e129 < i < 2.1499999999999999e153

   1. Initial program 89.1%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in b around inf 70.5%

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

   if -4.7000000000000002e-113 < i < 5.50000000000000033e-181

   1. Initial program 88.2%

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

   2. Taylor expanded in y around 0 77.3%

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

   3. Taylor expanded in j around 0 62.3%

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

   4. Taylor expanded in a around inf 60.0%

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

      1. associate-*r* 60.0%

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

      2. *-commutative 60.0%

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

      3. *-commutative 60.0%

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

      4. *-commutative 60.0%

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

   6. Simplified 60.0%

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

   if 1.34999999999999995e76 < i < 2e129 or 2.1499999999999999e153 < i

   1. Initial program 85.7%

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

   2. Taylor expanded in y around 0 91.4%

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

   3. Taylor expanded in j around 0 86.9%

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

   4. Taylor expanded in b around 0 78.4%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;i \leq -5.3 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-113}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+76} \lor \neg \left(i \leq 2 \cdot 10^{+129}\right) \land i \leq 2.15 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 9: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ t_3 := b \cdot c + t_1\\ t_4 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+31}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-214}:\\ \;\;\;\;t_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a 4.0))))
        (t_3 (+ (* b c) t_1))
        (t_4 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -6.6e+31)
     t_4
     (if (<= x -1.1e-46)
       t_3
       (if (<= x -6.8e-203)
         t_2
         (if (<= x -3.3e-214)
           (+ t_1 (* (* t a) -4.0))
           (if (<= x -2.55e-228)
             t_3
             (if (<= x 8.5e-284)
               t_2
               (if (<= x 3.1e-225) t_3 (if (<= x 3.8e+27) t_2 t_4))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (a * 4.0));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -6.6e+31) {
		tmp = t_4;
	} else if (x <= -1.1e-46) {
		tmp = t_3;
	} else if (x <= -6.8e-203) {
		tmp = t_2;
	} else if (x <= -3.3e-214) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if (x <= -2.55e-228) {
		tmp = t_3;
	} else if (x <= 8.5e-284) {
		tmp = t_2;
	} else if (x <= 3.1e-225) {
		tmp = t_3;
	} else if (x <= 3.8e+27) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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.
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) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) - (t * (a * 4.0d0))
    t_3 = (b * c) + t_1
    t_4 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-6.6d+31)) then
        tmp = t_4
    else if (x <= (-1.1d-46)) then
        tmp = t_3
    else if (x <= (-6.8d-203)) then
        tmp = t_2
    else if (x <= (-3.3d-214)) then
        tmp = t_1 + ((t * a) * (-4.0d0))
    else if (x <= (-2.55d-228)) then
        tmp = t_3
    else if (x <= 8.5d-284) then
        tmp = t_2
    else if (x <= 3.1d-225) then
        tmp = t_3
    else if (x <= 3.8d+27) then
        tmp = t_2
    else
        tmp = t_4
    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;
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 * (a * 4.0));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -6.6e+31) {
		tmp = t_4;
	} else if (x <= -1.1e-46) {
		tmp = t_3;
	} else if (x <= -6.8e-203) {
		tmp = t_2;
	} else if (x <= -3.3e-214) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if (x <= -2.55e-228) {
		tmp = t_3;
	} else if (x <= 8.5e-284) {
		tmp = t_2;
	} else if (x <= 3.1e-225) {
		tmp = t_3;
	} else if (x <= 3.8e+27) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (a * 4.0))
	t_3 = (b * c) + t_1
	t_4 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -6.6e+31:
		tmp = t_4
	elif x <= -1.1e-46:
		tmp = t_3
	elif x <= -6.8e-203:
		tmp = t_2
	elif x <= -3.3e-214:
		tmp = t_1 + ((t * a) * -4.0)
	elif x <= -2.55e-228:
		tmp = t_3
	elif x <= 8.5e-284:
		tmp = t_2
	elif x <= 3.1e-225:
		tmp = t_3
	elif x <= 3.8e+27:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) - Float64(t * Float64(a * 4.0)))
	t_3 = Float64(Float64(b * c) + t_1)
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -6.6e+31)
		tmp = t_4;
	elseif (x <= -1.1e-46)
		tmp = t_3;
	elseif (x <= -6.8e-203)
		tmp = t_2;
	elseif (x <= -3.3e-214)
		tmp = Float64(t_1 + Float64(Float64(t * a) * -4.0));
	elseif (x <= -2.55e-228)
		tmp = t_3;
	elseif (x <= 8.5e-284)
		tmp = t_2;
	elseif (x <= 3.1e-225)
		tmp = t_3;
	elseif (x <= 3.8e+27)
		tmp = t_2;
	else
		tmp = t_4;
	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])){:}
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 * (a * 4.0));
	t_3 = (b * c) + t_1;
	t_4 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -6.6e+31)
		tmp = t_4;
	elseif (x <= -1.1e-46)
		tmp = t_3;
	elseif (x <= -6.8e-203)
		tmp = t_2;
	elseif (x <= -3.3e-214)
		tmp = t_1 + ((t * a) * -4.0);
	elseif (x <= -2.55e-228)
		tmp = t_3;
	elseif (x <= 8.5e-284)
		tmp = t_2;
	elseif (x <= 3.1e-225)
		tmp = t_3;
	elseif (x <= 3.8e+27)
		tmp = t_2;
	else
		tmp = t_4;
	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.
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] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+31], t$95$4, If[LessEqual[x, -1.1e-46], t$95$3, If[LessEqual[x, -6.8e-203], t$95$2, If[LessEqual[x, -3.3e-214], N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.55e-228], t$95$3, If[LessEqual[x, 8.5e-284], t$95$2, If[LessEqual[x, 3.1e-225], t$95$3, If[LessEqual[x, 3.8e+27], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.59999999999999985e31 or 3.80000000000000022e27 < x

   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 84.8%

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

   4. Taylor expanded in x around inf 74.5%

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

   if -6.59999999999999985e31 < x < -1.1e-46 or -3.2999999999999998e-214 < x < -2.5500000000000001e-228 or 8.4999999999999995e-284 < x < 3.09999999999999996e-225

   1. Initial program 97.0%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in b around inf 82.7%

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

   if -1.1e-46 < x < -6.7999999999999998e-203 or -2.5500000000000001e-228 < x < 8.4999999999999995e-284 or 3.09999999999999996e-225 < x < 3.80000000000000022e27

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 86.2%

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

   3. Taylor expanded in j around 0 75.5%

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

   4. Taylor expanded in a around inf 66.5%

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

      1. associate-*r* 66.5%

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

      2. *-commutative 66.5%

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

      3. *-commutative 66.5%

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

      4. *-commutative 66.5%

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

   6. Simplified 66.5%

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

   if -6.7999999999999998e-203 < x < -3.2999999999999998e-214

   1. Initial program 100.0%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 91.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 10: 86.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))))
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
end

Wolfram

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

Derivation

1. Initial program 88.3%

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

3. Simplified 89.6%

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

4. Final simplification 89.6%

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

Alternative 11: 62.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + t_1\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -2.2e+47)
     t_3
     (if (<= x -5.1e-14)
       (+ (* 18.0 (* x (* y (* z t)))) t_1)
       (if (<= x 8.4e-284)
         t_2
         (if (<= x 3.5e-225) (+ (* b c) t_1) (if (<= x 6e+26) t_2 t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.2e+47) {
		tmp = t_3;
	} else if (x <= -5.1e-14) {
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	} else if (x <= 8.4e-284) {
		tmp = t_2;
	} else if (x <= 3.5e-225) {
		tmp = (b * c) + t_1;
	} else if (x <= 6e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))
    t_3 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-2.2d+47)) then
        tmp = t_3
    else if (x <= (-5.1d-14)) then
        tmp = (18.0d0 * (x * (y * (z * t)))) + t_1
    else if (x <= 8.4d-284) then
        tmp = t_2
    else if (x <= 3.5d-225) then
        tmp = (b * c) + t_1
    else if (x <= 6d+26) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.2e+47) {
		tmp = t_3;
	} else if (x <= -5.1e-14) {
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	} else if (x <= 8.4e-284) {
		tmp = t_2;
	} else if (x <= 3.5e-225) {
		tmp = (b * c) + t_1;
	} else if (x <= 6e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) - ((4.0 * (t * a)) + (4.0 * (x * i)))
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -2.2e+47:
		tmp = t_3
	elif x <= -5.1e-14:
		tmp = (18.0 * (x * (y * (z * t)))) + t_1
	elif x <= 8.4e-284:
		tmp = t_2
	elif x <= 3.5e-225:
		tmp = (b * c) + t_1
	elif x <= 6e+26:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i))))
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -2.2e+47)
		tmp = t_3;
	elseif (x <= -5.1e-14)
		tmp = Float64(Float64(18.0 * Float64(x * Float64(y * Float64(z * t)))) + t_1);
	elseif (x <= 8.4e-284)
		tmp = t_2;
	elseif (x <= 3.5e-225)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 6e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -2.2e+47)
		tmp = t_3;
	elseif (x <= -5.1e-14)
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	elseif (x <= 8.4e-284)
		tmp = t_2;
	elseif (x <= 3.5e-225)
		tmp = (b * c) + t_1;
	elseif (x <= 6e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+47], t$95$3, If[LessEqual[x, -5.1e-14], N[(N[(18.0 * N[(x * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 8.4e-284], t$95$2, If[LessEqual[x, 3.5e-225], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 6e+26], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1999999999999999e47 or 5.99999999999999994e26 < x

   1. Initial program 75.8%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   if -2.1999999999999999e47 < x < -5.0999999999999997e-14

   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 92.9%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 85.9%

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

      3. associate-*l* 78.8%

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

   6. Simplified 78.8%

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

   if -5.0999999999999997e-14 < x < 8.39999999999999965e-284 or 3.4999999999999997e-225 < x < 5.99999999999999994e26

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 87.1%

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

   3. Taylor expanded in j around 0 73.1%

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

   if 8.39999999999999965e-284 < x < 3.4999999999999997e-225

   1. Initial program 93.8%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around inf 81.3%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 12: 79.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.48 \cdot 10^{+147} \lor \neg \left(x \leq 2 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.48e+147) (not (<= x 2e+126)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.48e+147) || !(x <= 2e+126)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.48d+147)) .or. (.not. (x <= 2d+126))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.48e+147) || !(x <= 2e+126)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.48e+147) or not (x <= 2e+126):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.48e+147) || !(x <= 2e+126))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.48e+147) || ~((x <= 2e+126)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.48e+147], N[Not[LessEqual[x, 2e+126]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.48000000000000002e147 or 1.99999999999999985e126 < x

   1. Initial program 75.0%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in x around inf 85.7%

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

   if -1.48000000000000002e147 < x < 1.99999999999999985e126

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 82.8%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.48 \cdot 10^{+147} \lor \neg \left(x \leq 2 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 13: 58.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a 4.0))))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -3.8e+45)
     t_3
     (if (<= x -2.5e-14)
       (+ (* 18.0 (* x (* y (* z t)))) t_1)
       (if (<= x 7.2e-284)
         t_2
         (if (<= x 8.5e-225) (+ (* b c) t_1) (if (<= x 1.1e+27) t_2 t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (a * 4.0));
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.8e+45) {
		tmp = t_3;
	} else if (x <= -2.5e-14) {
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	} else if (x <= 7.2e-284) {
		tmp = t_2;
	} else if (x <= 8.5e-225) {
		tmp = (b * c) + t_1;
	} else if (x <= 1.1e+27) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * (a * 4.0d0))
    t_3 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-3.8d+45)) then
        tmp = t_3
    else if (x <= (-2.5d-14)) then
        tmp = (18.0d0 * (x * (y * (z * t)))) + t_1
    else if (x <= 7.2d-284) then
        tmp = t_2
    else if (x <= 8.5d-225) then
        tmp = (b * c) + t_1
    else if (x <= 1.1d+27) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * (a * 4.0));
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.8e+45) {
		tmp = t_3;
	} else if (x <= -2.5e-14) {
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	} else if (x <= 7.2e-284) {
		tmp = t_2;
	} else if (x <= 8.5e-225) {
		tmp = (b * c) + t_1;
	} else if (x <= 1.1e+27) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (a * 4.0))
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -3.8e+45:
		tmp = t_3
	elif x <= -2.5e-14:
		tmp = (18.0 * (x * (y * (z * t)))) + t_1
	elif x <= 7.2e-284:
		tmp = t_2
	elif x <= 8.5e-225:
		tmp = (b * c) + t_1
	elif x <= 1.1e+27:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) - Float64(t * Float64(a * 4.0)))
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -3.8e+45)
		tmp = t_3;
	elseif (x <= -2.5e-14)
		tmp = Float64(Float64(18.0 * Float64(x * Float64(y * Float64(z * t)))) + t_1);
	elseif (x <= 7.2e-284)
		tmp = t_2;
	elseif (x <= 8.5e-225)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 1.1e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (a * 4.0));
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -3.8e+45)
		tmp = t_3;
	elseif (x <= -2.5e-14)
		tmp = (18.0 * (x * (y * (z * t)))) + t_1;
	elseif (x <= 7.2e-284)
		tmp = t_2;
	elseif (x <= 8.5e-225)
		tmp = (b * c) + t_1;
	elseif (x <= 1.1e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+45], t$95$3, If[LessEqual[x, -2.5e-14], N[(N[(18.0 * N[(x * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 7.2e-284], t$95$2, If[LessEqual[x, 8.5e-225], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.1e+27], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8000000000000002e45 or 1.0999999999999999e27 < x

   1. Initial program 75.8%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   if -3.8000000000000002e45 < x < -2.5000000000000001e-14

   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 92.9%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 85.9%

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

      3. associate-*l* 78.8%

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

   6. Simplified 78.8%

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

   if -2.5000000000000001e-14 < x < 7.2000000000000004e-284 or 8.4999999999999998e-225 < x < 1.0999999999999999e27

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 87.1%

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

   3. Taylor expanded in j around 0 73.1%

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

   4. Taylor expanded in a around inf 65.1%

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

      1. associate-*r* 65.1%

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

      2. *-commutative 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

   6. Simplified 65.1%

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

   if 7.2000000000000004e-284 < x < 8.4999999999999998e-225

   1. Initial program 93.8%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around inf 81.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 14: 48.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;t_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 a) (- 4.0)) (* 4.0 (* x i)))))
   (if (<= c -1.4e-123)
     (+ (* b c) t_1)
     (if (<= c 9.8e-147)
       t_2
       (if (<= c 1.25e-58)
         (+ t_1 (* (* x i) -4.0))
         (if (<= c 7.5e+134) t_2 (- (* b c) (* x (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * a) * -4.0) - (4.0 * (x * i));
	double tmp;
	if (c <= -1.4e-123) {
		tmp = (b * c) + t_1;
	} else if (c <= 9.8e-147) {
		tmp = t_2;
	} else if (c <= 1.25e-58) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (c <= 7.5e+134) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * a) * -4.0d0) - (4.0d0 * (x * i))
    if (c <= (-1.4d-123)) then
        tmp = (b * c) + t_1
    else if (c <= 9.8d-147) then
        tmp = t_2
    else if (c <= 1.25d-58) then
        tmp = t_1 + ((x * i) * (-4.0d0))
    else if (c <= 7.5d+134) then
        tmp = t_2
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * a) * -4.0) - (4.0 * (x * i));
	double tmp;
	if (c <= -1.4e-123) {
		tmp = (b * c) + t_1;
	} else if (c <= 9.8e-147) {
		tmp = t_2;
	} else if (c <= 1.25e-58) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (c <= 7.5e+134) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * a) * -4.0) - (4.0 * (x * i))
	tmp = 0
	if c <= -1.4e-123:
		tmp = (b * c) + t_1
	elif c <= 9.8e-147:
		tmp = t_2
	elif c <= 1.25e-58:
		tmp = t_1 + ((x * i) * -4.0)
	elif c <= 7.5e+134:
		tmp = t_2
	else:
		tmp = (b * c) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(Float64(t * a) * Float64(-4.0)) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (c <= -1.4e-123)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (c <= 9.8e-147)
		tmp = t_2;
	elseif (c <= 1.25e-58)
		tmp = Float64(t_1 + Float64(Float64(x * i) * -4.0));
	elseif (c <= 7.5e+134)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * a) * -4.0) - (4.0 * (x * i));
	tmp = 0.0;
	if (c <= -1.4e-123)
		tmp = (b * c) + t_1;
	elseif (c <= 9.8e-147)
		tmp = t_2;
	elseif (c <= 1.25e-58)
		tmp = t_1 + ((x * i) * -4.0);
	elseif (c <= 7.5e+134)
		tmp = t_2;
	else
		tmp = (b * c) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(N[(t * a), $MachinePrecision] * (-4.0)), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.4e-123], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 9.8e-147], t$95$2, If[LessEqual[c, 1.25e-58], N[(t$95$1 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+134], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.3999999999999999e-123

   1. Initial program 84.1%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in b around inf 47.6%

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

   if -1.3999999999999999e-123 < c < 9.8000000000000001e-147 or 1.24999999999999994e-58 < c < 7.5000000000000001e134

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 75.0%

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

   3. Taylor expanded in j around 0 58.0%

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

   4. Taylor expanded in b around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   if 9.8000000000000001e-147 < c < 1.24999999999999994e-58

   1. Initial program 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in i around inf 67.3%

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

      1. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   if 7.5000000000000001e134 < c

   1. Initial program 88.4%

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

   2. Taylor expanded in y around 0 79.4%

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

   3. Taylor expanded in j around 0 72.5%

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

   4. Taylor expanded in a around 0 55.4%

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

      1. associate-*r* 55.4%

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

      2. *-commutative 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]

Alternative 15: 47.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ t_2 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* t (* a 4.0)))) (t_2 (+ (* b c) (* j (* k -27.0)))))
   (if (<= x -1.16e+142)
     (* x (* 18.0 (* z (* y t))))
     (if (<= x -2.3e-44)
       t_2
       (if (<= x 2.2e-284)
         t_1
         (if (<= x 9.5e-226)
           t_2
           (if (<= x 2.8e+46) t_1 (* x (* 18.0 (* y (* z t)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -1.16e+142) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= -2.3e-44) {
		tmp = t_2;
	} else if (x <= 2.2e-284) {
		tmp = t_1;
	} else if (x <= 9.5e-226) {
		tmp = t_2;
	} else if (x <= 2.8e+46) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (t * (a * 4.0d0))
    t_2 = (b * c) + (j * (k * (-27.0d0)))
    if (x <= (-1.16d+142)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if (x <= (-2.3d-44)) then
        tmp = t_2
    else if (x <= 2.2d-284) then
        tmp = t_1
    else if (x <= 9.5d-226) then
        tmp = t_2
    else if (x <= 2.8d+46) then
        tmp = t_1
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -1.16e+142) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= -2.3e-44) {
		tmp = t_2;
	} else if (x <= 2.2e-284) {
		tmp = t_1;
	} else if (x <= 9.5e-226) {
		tmp = t_2;
	} else if (x <= 2.8e+46) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (t * (a * 4.0))
	t_2 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if x <= -1.16e+142:
		tmp = x * (18.0 * (z * (y * t)))
	elif x <= -2.3e-44:
		tmp = t_2
	elif x <= 2.2e-284:
		tmp = t_1
	elif x <= 9.5e-226:
		tmp = t_2
	elif x <= 2.8e+46:
		tmp = t_1
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))
	t_2 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -1.16e+142)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (x <= -2.3e-44)
		tmp = t_2;
	elseif (x <= 2.2e-284)
		tmp = t_1;
	elseif (x <= 9.5e-226)
		tmp = t_2;
	elseif (x <= 2.8e+46)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (t * (a * 4.0));
	t_2 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -1.16e+142)
		tmp = x * (18.0 * (z * (y * t)));
	elseif (x <= -2.3e-44)
		tmp = t_2;
	elseif (x <= 2.2e-284)
		tmp = t_1;
	elseif (x <= 9.5e-226)
		tmp = t_2;
	elseif (x <= 2.8e+46)
		tmp = t_1;
	else
		tmp = x * (18.0 * (y * (z * t)));
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.16e+142], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-44], t$95$2, If[LessEqual[x, 2.2e-284], t$95$1, If[LessEqual[x, 9.5e-226], t$95$2, If[LessEqual[x, 2.8e+46], t$95$1, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.16000000000000003e142

   1. Initial program 70.2%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 85.8%

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

   5. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 48.3%

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

   7. Simplified 48.3%

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

   if -1.16000000000000003e142 < x < -2.29999999999999998e-44 or 2.2000000000000001e-284 < x < 9.5000000000000007e-226

   1. Initial program 90.9%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in b around inf 64.8%

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

   if -2.29999999999999998e-44 < x < 2.2000000000000001e-284 or 9.5000000000000007e-226 < x < 2.80000000000000018e46

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 87.3%

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

   3. Taylor expanded in j around 0 73.4%

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

   4. Taylor expanded in a around inf 64.2%

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

      1. associate-*r* 64.2%

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

      2. *-commutative 64.2%

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

      3. *-commutative 64.2%

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

      4. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   if 2.80000000000000018e46 < x

   1. Initial program 76.8%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around inf 75.2%

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

   5. Taylor expanded in t around inf 47.6%

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

      1. *-commutative 47.6%

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

      2. associate-*l* 47.6%

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

   7. Simplified 47.6%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-44}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 16: 71.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+141} \lor \neg \left(x \leq 3.6 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.25e+141) (not (<= x 3.6e+34)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.25e+141) || !(x <= 3.6e+34)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.25d+141)) .or. (.not. (x <= 3.6d+34))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.25e+141) || !(x <= 3.6e+34)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.25e+141) or not (x <= 3.6e+34):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.25e+141) || !(x <= 3.6e+34))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.25e+141) || ~((x <= 3.6e+34)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2.25e+141], N[Not[LessEqual[x, 3.6e+34]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2500000000000001e141 or 3.6e34 < x

   1. Initial program 74.1%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around inf 80.3%

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

   if -2.2500000000000001e141 < x < 3.6e34

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 76.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+141} \lor \neg \left(x \leq 3.6 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 17: 43.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.36 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= x -1.36e+141)
     (* x (* 18.0 (* z (* y t))))
     (if (<= x -1.32e-132)
       t_1
       (if (<= x -5.1e-201)
         (* t (* a -4.0))
         (if (<= x 3.4e-36) t_1 (* i (* x -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -1.36e+141) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= -1.32e-132) {
		tmp = t_1;
	} else if (x <= -5.1e-201) {
		tmp = t * (a * -4.0);
	} else if (x <= 3.4e-36) {
		tmp = t_1;
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (x <= (-1.36d+141)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if (x <= (-1.32d-132)) then
        tmp = t_1
    else if (x <= (-5.1d-201)) then
        tmp = t * (a * (-4.0d0))
    else if (x <= 3.4d-36) then
        tmp = t_1
    else
        tmp = i * (x * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -1.36e+141) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= -1.32e-132) {
		tmp = t_1;
	} else if (x <= -5.1e-201) {
		tmp = t * (a * -4.0);
	} else if (x <= 3.4e-36) {
		tmp = t_1;
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if x <= -1.36e+141:
		tmp = x * (18.0 * (z * (y * t)))
	elif x <= -1.32e-132:
		tmp = t_1
	elif x <= -5.1e-201:
		tmp = t * (a * -4.0)
	elif x <= 3.4e-36:
		tmp = t_1
	else:
		tmp = i * (x * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -1.36e+141)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (x <= -1.32e-132)
		tmp = t_1;
	elseif (x <= -5.1e-201)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (x <= 3.4e-36)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(x * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -1.36e+141)
		tmp = x * (18.0 * (z * (y * t)));
	elseif (x <= -1.32e-132)
		tmp = t_1;
	elseif (x <= -5.1e-201)
		tmp = t * (a * -4.0);
	elseif (x <= 3.4e-36)
		tmp = t_1;
	else
		tmp = i * (x * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.36e+141], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.32e-132], t$95$1, If[LessEqual[x, -5.1e-201], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-36], t$95$1, N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.36e141

   1. Initial program 70.2%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 85.8%

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

   5. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 48.3%

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

   7. Simplified 48.3%

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

   if -1.36e141 < x < -1.32000000000000004e-132 or -5.1000000000000001e-201 < x < 3.4000000000000003e-36

   1. Initial program 94.1%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in b around inf 55.8%

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

   if -1.32000000000000004e-132 < x < -5.1000000000000001e-201

   1. Initial program 99.8%

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

   3. Simplified 92.8%

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

      1. add-cube-cbrt 92.7%

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

      2. pow3 92.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 92.7%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 92.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in a around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-*l* 63.1%

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

   8. Simplified 63.1%

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

   if 3.4000000000000003e-36 < x

   1. Initial program 81.2%

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

   3. Simplified 86.9%

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

      1. add-cube-cbrt 86.8%

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

      2. pow3 86.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 86.8%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 86.8%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in x around inf 43.4%

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

      1. *-commutative 43.4%

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

      2. associate-*r* 43.4%

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

      3. *-commutative 43.4%

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

   8. Simplified 43.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-132}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 18: 46.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-180}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;y \leq 0.00018:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* x (* 4.0 i)))))
   (if (<= y -1.6e+134)
     (* x (* 18.0 (* z (* y t))))
     (if (<= y -3.8e+19)
       t_1
       (if (<= y 1.35e-180)
         (- (* b c) (* t (* a 4.0)))
         (if (<= y 0.00018) t_1 (* x (* 18.0 (* y (* z t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (y <= -1.6e+134) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (y <= -3.8e+19) {
		tmp = t_1;
	} else if (y <= 1.35e-180) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (y <= 0.00018) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (x * (4.0d0 * i))
    if (y <= (-1.6d+134)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if (y <= (-3.8d+19)) then
        tmp = t_1
    else if (y <= 1.35d-180) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else if (y <= 0.00018d0) then
        tmp = t_1
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (y <= -1.6e+134) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (y <= -3.8e+19) {
		tmp = t_1;
	} else if (y <= 1.35e-180) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (y <= 0.00018) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if y <= -1.6e+134:
		tmp = x * (18.0 * (z * (y * t)))
	elif y <= -3.8e+19:
		tmp = t_1
	elif y <= 1.35e-180:
		tmp = (b * c) - (t * (a * 4.0))
	elif y <= 0.00018:
		tmp = t_1
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (y <= -1.6e+134)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (y <= -3.8e+19)
		tmp = t_1;
	elseif (y <= 1.35e-180)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	elseif (y <= 0.00018)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (y <= -1.6e+134)
		tmp = x * (18.0 * (z * (y * t)));
	elseif (y <= -3.8e+19)
		tmp = t_1;
	elseif (y <= 1.35e-180)
		tmp = (b * c) - (t * (a * 4.0));
	elseif (y <= 0.00018)
		tmp = t_1;
	else
		tmp = x * (18.0 * (y * (z * t)));
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+134], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e+19], t$95$1, If[LessEqual[y, 1.35e-180], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00018], t$95$1, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e134

   1. Initial program 86.2%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around inf 58.4%

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

   5. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 55.0%

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

   7. Simplified 55.0%

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

   if -1.6e134 < y < -3.8e19 or 1.35000000000000007e-180 < y < 1.80000000000000011e-4

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 79.9%

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

   3. Taylor expanded in j around 0 60.6%

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

   4. Taylor expanded in a around 0 52.6%

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

      1. associate-*r* 52.6%

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

      2. *-commutative 52.6%

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

   6. Simplified 52.6%

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

   if -3.8e19 < y < 1.35000000000000007e-180

   1. Initial program 93.8%

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

   2. Taylor expanded in y around 0 88.5%

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

   3. Taylor expanded in j around 0 75.5%

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

   4. Taylor expanded in a around inf 58.1%

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

      1. associate-*r* 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

      4. *-commutative 58.1%

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

   6. Simplified 58.1%

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

   if 1.80000000000000011e-4 < y

   1. Initial program 80.5%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around inf 42.1%

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

   5. Taylor expanded in t around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*l* 33.7%

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

   7. Simplified 33.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-180}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;y \leq 0.00018:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 19: 31.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-62}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= c -2.05e-85)
     (* b c)
     (if (<= c 4.3e-148)
       t_1
       (if (<= c 1.8e-62)
         (* k (* j -27.0))
         (if (<= c 2.5e+136) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (c <= -2.05e-85) {
		tmp = b * c;
	} else if (c <= 4.3e-148) {
		tmp = t_1;
	} else if (c <= 1.8e-62) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.5e+136) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (c <= (-2.05d-85)) then
        tmp = b * c
    else if (c <= 4.3d-148) then
        tmp = t_1
    else if (c <= 1.8d-62) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 2.5d+136) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (c <= -2.05e-85) {
		tmp = b * c;
	} else if (c <= 4.3e-148) {
		tmp = t_1;
	} else if (c <= 1.8e-62) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.5e+136) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if c <= -2.05e-85:
		tmp = b * c
	elif c <= 4.3e-148:
		tmp = t_1
	elif c <= 1.8e-62:
		tmp = k * (j * -27.0)
	elif c <= 2.5e+136:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (c <= -2.05e-85)
		tmp = Float64(b * c);
	elseif (c <= 4.3e-148)
		tmp = t_1;
	elseif (c <= 1.8e-62)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 2.5e+136)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (c <= -2.05e-85)
		tmp = b * c;
	elseif (c <= 4.3e-148)
		tmp = t_1;
	elseif (c <= 1.8e-62)
		tmp = k * (j * -27.0);
	elseif (c <= 2.5e+136)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.05e-85], N[(b * c), $MachinePrecision], If[LessEqual[c, 4.3e-148], t$95$1, If[LessEqual[c, 1.8e-62], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+136], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.04999999999999997e-85 or 2.5000000000000001e136 < c

   1. Initial program 85.8%

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

   3. Simplified 86.8%

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

      1. add-cube-cbrt 86.8%

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

      2. pow3 86.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 86.8%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 86.8%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 39.4%

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

   if -2.04999999999999997e-85 < c < 4.2999999999999998e-148 or 1.8e-62 < c < 2.5000000000000001e136

   1. Initial program 90.9%

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

   3. Simplified 92.7%

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

      1. add-cube-cbrt 92.5%

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

      2. pow3 92.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 92.5%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 92.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in a around inf 28.4%

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

      1. *-commutative 28.4%

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

      2. *-commutative 28.4%

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

      3. associate-*l* 28.4%

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

   8. Simplified 28.4%

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

   if 4.2999999999999998e-148 < c < 1.8e-62

   1. Initial program 87.4%

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

   3. Simplified 87.4%

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

      1. add-cube-cbrt 87.4%

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

      2. pow3 87.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 87.4%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 87.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in j around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*r* 47.3%

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

   8. Simplified 47.3%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-62}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+198} \lor \neg \left(b \cdot c \leq 2.75 \cdot 10^{+100}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -6.6e+198) (not (<= (* b c) 2.75e+100)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -6.6e+198) || !((b * c) <= 2.75e+100)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-6.6d+198)) .or. (.not. ((b * c) <= 2.75d+100))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -6.6e+198) || !((b * c) <= 2.75e+100)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -6.6e+198) or not ((b * c) <= 2.75e+100):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -6.6e+198) || !(Float64(b * c) <= 2.75e+100))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -6.6e+198) || ~(((b * c) <= 2.75e+100)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -6.6e+198], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.75e+100]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -6.59999999999999988e198 or 2.7500000000000001e100 < (*.f64 b c)

   1. Initial program 86.2%

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

   3. Simplified 88.9%

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

      1. add-cube-cbrt 88.8%

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

      2. pow3 88.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.8%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 68.3%

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

   if -6.59999999999999988e198 < (*.f64 b c) < 2.7500000000000001e100

   1. Initial program 89.2%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in j around inf 23.5%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+198} \lor \neg \left(b \cdot c \leq 2.75 \cdot 10^{+100}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 21: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.2 \cdot 10^{+200} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+98}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.2e+200) (not (<= (* b c) 4e+98)))
   (* b c)
   (* k (* j -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.2e+200) || !((b * c) <= 4e+98)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1.2d+200)) .or. (.not. ((b * c) <= 4d+98))) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.2e+200) || !((b * c) <= 4e+98)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.2e+200) or not ((b * c) <= 4e+98):
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.2e+200) || !(Float64(b * c) <= 4e+98))
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.2e+200) || ~(((b * c) <= 4e+98)))
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.2e+200], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4e+98]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.2e200 or 3.99999999999999999e98 < (*.f64 b c)

   1. Initial program 86.2%

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

   3. Simplified 88.9%

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

      1. add-cube-cbrt 88.8%

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

      2. pow3 88.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.8%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 88.8%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 68.3%

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

   if -1.2e200 < (*.f64 b c) < 3.99999999999999999e98

   1. Initial program 89.2%

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

   3. Simplified 89.9%

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

      1. add-cube-cbrt 89.9%

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

      2. pow3 89.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 89.9%

         \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 89.9%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in j around inf 23.5%

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

      1. *-commutative 23.5%

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

      2. *-commutative 23.5%

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

      3. associate-*r* 23.5%

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

   8. Simplified 23.5%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.2 \cdot 10^{+200} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+98}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 22: 24.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.3%

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

3. Simplified 89.6%

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

   1. add-cube-cbrt 89.6%

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

   2. pow3 89.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. *-commutative 89.6%

      \[\leadsto \left(t \cdot \left({\left(\sqrt[3]{\color{blue}{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}}\right)}^{3} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

5. Applied egg-rr 89.6%

   \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\sqrt[3]{\left(y \cdot z\right) \cdot \left(x \cdot 18\right)}\right)}^{3}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

6. Taylor expanded in b around inf 24.5%

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

7. Final simplification 24.5%

   \[\leadsto b \cdot c \]

Developer target: 89.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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