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

Percentage Accurate: 85.3% → 91.2%

Time: 50.6s

Alternatives: 24

Speedup: 0.9×

• 50.8% 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: 85.3% 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: 91.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

   3. Simplified 95.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 19.2%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. associate-*r* 69.5%

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

      3. metadata-eval 69.5%

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 92.8%

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

Alternative 2: 91.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

   3. Simplified 95.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 19.2%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. associate-*r* 69.5%

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

      3. metadata-eval 69.5%

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

   7. Applied egg-rr 69.5%

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

4. Final simplification 92.8%

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

Alternative 3: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))))
   (if (<= t -5.7e+24)
     t_1
     (if (<= t 1.85e-175)
       (- (* b c) (+ (* (* j k) 27.0) (* 4.0 (* x i))))
       (if (<= t 3.9e-62)
         (- (* b c) (* x (- (* 4.0 i) (* 18.0 (* t (* y z))))))
         (if (<= t 1.1e+78)
           (- (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b))) (* k (* j 27.0)))
           t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -5.7e+24) {
		tmp = t_1;
	} else if (t <= 1.85e-175) {
		tmp = (b * c) - (((j * k) * 27.0) + (4.0 * (x * i)));
	} else if (t <= 3.9e-62) {
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	} else if (t <= 1.1e+78) {
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    if (t <= (-5.7d+24)) then
        tmp = t_1
    else if (t <= 1.85d-175) then
        tmp = (b * c) - (((j * k) * 27.0d0) + (4.0d0 * (x * i)))
    else if (t <= 3.9d-62) then
        tmp = (b * c) - (x * ((4.0d0 * i) - (18.0d0 * (t * (y * z)))))
    else if (t <= 1.1d+78) then
        tmp = (b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))) - (k * (j * 27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -5.7e+24) {
		tmp = t_1;
	} else if (t <= 1.85e-175) {
		tmp = (b * c) - (((j * k) * 27.0) + (4.0 * (x * i)));
	} else if (t <= 3.9e-62) {
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	} else if (t <= 1.1e+78) {
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	tmp = 0
	if t <= -5.7e+24:
		tmp = t_1
	elif t <= 1.85e-175:
		tmp = (b * c) - (((j * k) * 27.0) + (4.0 * (x * i)))
	elif t <= 3.9e-62:
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))
	elif t <= 1.1e+78:
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - (k * (j * 27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -5.7e+24)
		tmp = t_1;
	elseif (t <= 1.85e-175)
		tmp = Float64(Float64(b * c) - Float64(Float64(Float64(j * k) * 27.0) + Float64(4.0 * Float64(x * i))));
	elseif (t <= 3.9e-62)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(Float64(4.0 * i) - Float64(18.0 * Float64(t * Float64(y * z))))));
	elseif (t <= 1.1e+78)
		tmp = Float64(Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -5.7e+24)
		tmp = t_1;
	elseif (t <= 1.85e-175)
		tmp = (b * c) - (((j * k) * 27.0) + (4.0 * (x * i)));
	elseif (t <= 3.9e-62)
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	elseif (t <= 1.1e+78)
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - (k * (j * 27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+24], t$95$1, If[LessEqual[t, 1.85e-175], N[(N[(b * c), $MachinePrecision] - N[(N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-62], N[(N[(b * c), $MachinePrecision] - N[(x * N[(N[(4.0 * i), $MachinePrecision] - N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+78], N[(N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.7000000000000005e24 or 1.10000000000000007e78 < t

   1. Initial program 83.8%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 83.0%

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

   if -5.7000000000000005e24 < t < 1.84999999999999999e-175

   1. Initial program 91.6%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t around 0 84.9%

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

   if 1.84999999999999999e-175 < t < 3.9000000000000003e-62

   1. Initial program 63.7%

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

   3. Taylor expanded in x around 0 75.4%

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

   4. Taylor expanded in a around 0 67.3%

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

   5. Taylor expanded in j around 0 71.5%

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

   if 3.9000000000000003e-62 < t < 1.10000000000000007e78

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in b around inf 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

      3. distribute-lft-out 81.0%

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

      4. distribute-lft-neg-in 81.0%

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

      5. metadata-eval 81.0%

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

      6. *-commutative 81.0%

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

   6. Simplified 81.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-175}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -5.1 \cdot 10^{+188}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-307}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-184}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -5.1e+188)
     (- (* b c) (* a (* t 4.0)))
     (if (<= (* b c) -1.55e-307)
       (* -4.0 (+ (* t a) (* x i)))
       (if (<= (* b c) 9.5e-184)
         (+ t_1 (* -4.0 (* x i)))
         (if (<= (* b c) 4.2e+123)
           (+ t_1 (* a (* t -4.0)))
           (- (* b c) (* x (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5.1e+188) {
		tmp = (b * c) - (a * (t * 4.0));
	} else if ((b * c) <= -1.55e-307) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 9.5e-184) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 4.2e+123) {
		tmp = t_1 + (a * (t * -4.0));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-5.1d+188)) then
        tmp = (b * c) - (a * (t * 4.0d0))
    else if ((b * c) <= (-1.55d-307)) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if ((b * c) <= 9.5d-184) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if ((b * c) <= 4.2d+123) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5.1e+188) {
		tmp = (b * c) - (a * (t * 4.0));
	} else if ((b * c) <= -1.55e-307) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 9.5e-184) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 4.2e+123) {
		tmp = t_1 + (a * (t * -4.0));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -5.1e+188:
		tmp = (b * c) - (a * (t * 4.0))
	elif (b * c) <= -1.55e-307:
		tmp = -4.0 * ((t * a) + (x * i))
	elif (b * c) <= 9.5e-184:
		tmp = t_1 + (-4.0 * (x * i))
	elif (b * c) <= 4.2e+123:
		tmp = t_1 + (a * (t * -4.0))
	else:
		tmp = (b * c) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -5.1e+188)
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	elseif (Float64(b * c) <= -1.55e-307)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (Float64(b * c) <= 9.5e-184)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 4.2e+123)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -5.1e+188)
		tmp = (b * c) - (a * (t * 4.0));
	elseif ((b * c) <= -1.55e-307)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif ((b * c) <= 9.5e-184)
		tmp = t_1 + (-4.0 * (x * i));
	elseif ((b * c) <= 4.2e+123)
		tmp = t_1 + (a * (t * -4.0));
	else
		tmp = (b * c) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.1e+188], N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.55e-307], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e-184], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+123], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -5.1000000000000002e188

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0 87.9%

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

   4. Taylor expanded in j around 0 87.9%

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

      1. distribute-lft-out 87.9%

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

      2. *-commutative 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in t around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*r* 87.9%

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

      3. *-commutative 87.9%

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

      4. *-commutative 87.9%

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

   9. Simplified 87.9%

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

   if -5.1000000000000002e188 < (*.f64 b c) < -1.5499999999999999e-307

   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. Add Preprocessing

   3. Taylor expanded in x around 0 73.3%

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

   4. Taylor expanded in j around 0 57.6%

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

      1. distribute-lft-out 57.6%

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

      2. *-commutative 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in b around 0 52.8%

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

   if -1.5499999999999999e-307 < (*.f64 b c) < 9.4999999999999991e-184

   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 93.3%

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

   5. Taylor expanded in i around inf 61.6%

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

   if 9.4999999999999991e-184 < (*.f64 b c) < 4.19999999999999988e123

   1. Initial program 85.5%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in a around inf 52.4%

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

      1. metadata-eval 52.4%

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

      2. distribute-lft-neg-in 52.4%

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

      3. *-commutative 52.4%

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

      4. associate-*l* 52.4%

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

      5. distribute-lft-neg-in 52.4%

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

      6. distribute-lft-neg-in 52.4%

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

      7. metadata-eval 52.4%

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

   7. Simplified 52.4%

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

   if 4.19999999999999988e123 < (*.f64 b c)

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0 63.4%

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

   4. Taylor expanded in j around 0 63.6%

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

      1. distribute-lft-out 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in t around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

      3. associate-*l* 63.6%

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

      4. *-commutative 63.6%

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

   9. Simplified 63.6%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.1 \cdot 10^{+188}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-307}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-184}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(b \cdot c - t \cdot \left(a \cdot 4 - t\_1\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -4.75 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+60}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (- (- (* b c) (* t (- (* a 4.0) t_1))) (* 4.0 (* x i)))))
   (if (<= t -4.75e-85)
     t_2
     (if (<= t 7e+60)
       (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* k (* j 27.0)))
       (if (<= t 7.5e+164)
         t_2
         (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = ((b * c) - (t * ((a * 4.0) - t_1))) - (4.0 * (x * i));
	double tmp;
	if (t <= -4.75e-85) {
		tmp = t_2;
	} else if (t <= 7e+60) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if (t <= 7.5e+164) {
		tmp = t_2;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = ((b * c) - (t * ((a * 4.0d0) - t_1))) - (4.0d0 * (x * i))
    if (t <= (-4.75d-85)) then
        tmp = t_2
    else if (t <= 7d+60) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - (k * (j * 27.0d0))
    else if (t <= 7.5d+164) then
        tmp = t_2
    else
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = ((b * c) - (t * ((a * 4.0) - t_1))) - (4.0 * (x * i));
	double tmp;
	if (t <= -4.75e-85) {
		tmp = t_2;
	} else if (t <= 7e+60) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else if (t <= 7.5e+164) {
		tmp = t_2;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = ((b * c) - (t * ((a * 4.0) - t_1))) - (4.0 * (x * i))
	tmp = 0
	if t <= -4.75e-85:
		tmp = t_2
	elif t <= 7e+60:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0))
	elif t <= 7.5e+164:
		tmp = t_2
	else:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - t_1))) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (t <= -4.75e-85)
		tmp = t_2;
	elseif (t <= 7e+60)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 7.5e+164)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = ((b * c) - (t * ((a * 4.0) - t_1))) - (4.0 * (x * i));
	tmp = 0.0;
	if (t <= -4.75e-85)
		tmp = t_2;
	elseif (t <= 7e+60)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	elseif (t <= 7.5e+164)
		tmp = t_2;
	else
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.75e-85], t$95$2, If[LessEqual[t, 7e+60], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+164], t$95$2, N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.74999999999999982e-85 or 7.0000000000000004e60 < t < 7.49999999999999976e164

   1. Initial program 90.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in j around 0 89.2%

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

   if -4.74999999999999982e-85 < t < 7.0000000000000004e60

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 85.6%

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

   if 7.49999999999999976e164 < t

   1. Initial program 68.3%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around inf 94.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.75 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+60}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+279}:\\ \;\;\;\;\left(b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right) - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{t \cdot a + x \cdot i}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) 5e+279)
   (-
    (- (* b c) (* x (- (* 4.0 i) (* 18.0 (* t (* y z))))))
    (+ (* (* j k) 27.0) (* 4.0 (* t a))))
   (* b (+ c (* -4.0 (/ (+ (* t a) (* x i)) b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= 5e+279) {
		tmp = ((b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))) - (((j * k) * 27.0) + (4.0 * (t * a)));
	} else {
		tmp = b * (c + (-4.0 * (((t * a) + (x * i)) / b)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= 5d+279) then
        tmp = ((b * c) - (x * ((4.0d0 * i) - (18.0d0 * (t * (y * z)))))) - (((j * k) * 27.0d0) + (4.0d0 * (t * a)))
    else
        tmp = b * (c + ((-4.0d0) * (((t * a) + (x * i)) / b)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= 5e+279) {
		tmp = ((b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))) - (((j * k) * 27.0) + (4.0 * (t * a)));
	} else {
		tmp = b * (c + (-4.0 * (((t * a) + (x * i)) / b)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= 5e+279:
		tmp = ((b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))) - (((j * k) * 27.0) + (4.0 * (t * a)))
	else:
		tmp = b * (c + (-4.0 * (((t * a) + (x * i)) / b)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= 5e+279)
		tmp = Float64(Float64(Float64(b * c) - Float64(x * Float64(Float64(4.0 * i) - Float64(18.0 * Float64(t * Float64(y * z)))))) - Float64(Float64(Float64(j * k) * 27.0) + Float64(4.0 * Float64(t * a))));
	else
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(Float64(Float64(t * a) + Float64(x * i)) / b))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= 5e+279)
		tmp = ((b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))) - (((j * k) * 27.0) + (4.0 * (t * a)));
	else
		tmp = b * (c + (-4.0 * (((t * a) + (x * i)) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 5e+279], N[(N[(N[(b * c), $MachinePrecision] - N[(x * N[(N[(4.0 * i), $MachinePrecision] - N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-4.0 * N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 5.0000000000000002e279

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 91.8%

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

   if 5.0000000000000002e279 < (*.f64 b c)

   1. Initial program 50.0%

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

   3. Taylor expanded in x around 0 57.1%

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

   4. Taylor expanded in j around 0 64.3%

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

      1. distribute-lft-out 64.3%

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

      2. *-commutative 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in b around inf 85.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 5 \cdot 10^{+279}:\\ \;\;\;\;\left(b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right) - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{t \cdot a + x \cdot i}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot t\_2\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(b \cdot c - t\_1\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot t\_2\right)\right) - \left(\left(j \cdot k\right) \cdot 27 + t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* t a))) (t_2 (* x (* y z))))
   (if (<= t -1.25e-82)
     (- (- (* b c) (* t (- (* a 4.0) (* 18.0 t_2)))) (* 4.0 (* x i)))
     (if (<= t 7.5e+77)
       (- (- (- (* b c) t_1) (* (* x 4.0) i)) (* k (* j 27.0)))
       (- (+ (* b c) (* 18.0 (* t t_2))) (+ (* (* j k) 27.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = x * (y * z);
	double tmp;
	if (t <= -1.25e-82) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_2)))) - (4.0 * (x * i));
	} else if (t <= 7.5e+77) {
		tmp = (((b * c) - t_1) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (18.0 * (t * t_2))) - (((j * k) * 27.0) + 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.
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 * (t * a)
    t_2 = x * (y * z)
    if (t <= (-1.25d-82)) then
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * t_2)))) - (4.0d0 * (x * i))
    else if (t <= 7.5d+77) then
        tmp = (((b * c) - t_1) - ((x * 4.0d0) * i)) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) + (18.0d0 * (t * t_2))) - (((j * k) * 27.0d0) + 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;
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 * (t * a);
	double t_2 = x * (y * z);
	double tmp;
	if (t <= -1.25e-82) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_2)))) - (4.0 * (x * i));
	} else if (t <= 7.5e+77) {
		tmp = (((b * c) - t_1) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (18.0 * (t * t_2))) - (((j * k) * 27.0) + 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (t * a)
	t_2 = x * (y * z)
	tmp = 0
	if t <= -1.25e-82:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_2)))) - (4.0 * (x * i))
	elif t <= 7.5e+77:
		tmp = (((b * c) - t_1) - ((x * 4.0) * i)) - (k * (j * 27.0))
	else:
		tmp = ((b * c) + (18.0 * (t * t_2))) - (((j * k) * 27.0) + 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (t <= -1.25e-82)
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * t_2)))) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 7.5e+77)
		tmp = Float64(Float64(Float64(Float64(b * c) - t_1) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_2))) - Float64(Float64(Float64(j * k) * 27.0) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (t * a);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (t <= -1.25e-82)
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_2)))) - (4.0 * (x * i));
	elseif (t <= 7.5e+77)
		tmp = (((b * c) - t_1) - ((x * 4.0) * i)) - (k * (j * 27.0));
	else
		tmp = ((b * c) + (18.0 * (t * t_2))) - (((j * k) * 27.0) + 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-82], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+77], N[(N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e-82

   1. Initial program 90.2%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in j around 0 87.7%

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

   if -1.25e-82 < t < 7.49999999999999955e77

   1. Initial program 85.0%

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

   3. Taylor expanded in x around 0 85.5%

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

   if 7.49999999999999955e77 < t

   1. Initial program 77.4%

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

   3. Taylor expanded in i around 0 87.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + -27 \cdot \frac{j \cdot k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -6e-45)
     t_1
     (if (<= t -1.8e-271)
       (+ (* j (* k -27.0)) (* -4.0 (* x i)))
       (if (<= t 2.4e-14)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= t 8.2e+62)
           (* t (+ (* a -4.0) (* -27.0 (/ (* j k) t))))
           t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e-45) {
		tmp = t_1;
	} else if (t <= -1.8e-271) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else if (t <= 2.4e-14) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 8.2e+62) {
		tmp = t * ((a * -4.0) + (-27.0 * ((j * k) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-6d-45)) then
        tmp = t_1
    else if (t <= (-1.8d-271)) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * i))
    else if (t <= 2.4d-14) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 8.2d+62) then
        tmp = t * ((a * (-4.0d0)) + ((-27.0d0) * ((j * k) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e-45) {
		tmp = t_1;
	} else if (t <= -1.8e-271) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else if (t <= 2.4e-14) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 8.2e+62) {
		tmp = t * ((a * -4.0) + (-27.0 * ((j * k) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -6e-45:
		tmp = t_1
	elif t <= -1.8e-271:
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i))
	elif t <= 2.4e-14:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 8.2e+62:
		tmp = t * ((a * -4.0) + (-27.0 * ((j * k) / t)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -6e-45)
		tmp = t_1;
	elseif (t <= -1.8e-271)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 2.4e-14)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 8.2e+62)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(-27.0 * Float64(Float64(j * k) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -6e-45)
		tmp = t_1;
	elseif (t <= -1.8e-271)
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	elseif (t <= 2.4e-14)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 8.2e+62)
		tmp = t * ((a * -4.0) + (-27.0 * ((j * k) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-45], t$95$1, If[LessEqual[t, -1.8e-271], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-14], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+62], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000022e-45 or 8.19999999999999967e62 < t

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in t around inf 73.7%

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

   if -6.00000000000000022e-45 < t < -1.7999999999999999e-271

   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 92.2%

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

   5. Taylor expanded in i around inf 62.7%

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

   if -1.7999999999999999e-271 < t < 2.4e-14

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0 79.5%

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

   4. Taylor expanded in j around 0 69.3%

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

      1. distribute-lft-out 69.3%

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

      2. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in t around 0 63.8%

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

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*l* 63.8%

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

      4. *-commutative 63.8%

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

   9. Simplified 63.8%

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

   if 2.4e-14 < t < 8.19999999999999967e62

   1. Initial program 87.5%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 69.3%

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

      1. metadata-eval 69.3%

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

      2. distribute-lft-neg-in 69.3%

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

      3. *-commutative 69.3%

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

      4. associate-*l* 69.3%

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

      5. distribute-lft-neg-in 69.3%

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

      6. distribute-lft-neg-in 69.3%

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

      7. metadata-eval 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in t around inf 69.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-271}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + -27 \cdot \frac{j \cdot k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} - j \cdot 27\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-198}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+102}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= c -3.5e-43)
     (* k (- (* b (/ c k)) (* j 27.0)))
     (if (<= c 3e-198)
       (* -4.0 (+ (* t a) (* x i)))
       (if (<= c 1.55e-32)
         (+ t_1 (* -4.0 (* x i)))
         (if (<= c 1.02e+102)
           (+ t_1 (* a (* t -4.0)))
           (- (* b c) (* x (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (c <= -3.5e-43) {
		tmp = k * ((b * (c / k)) - (j * 27.0));
	} else if (c <= 3e-198) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (c <= 1.55e-32) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (c <= 1.02e+102) {
		tmp = t_1 + (a * (t * -4.0));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (c <= (-3.5d-43)) then
        tmp = k * ((b * (c / k)) - (j * 27.0d0))
    else if (c <= 3d-198) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if (c <= 1.55d-32) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if (c <= 1.02d+102) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (c <= -3.5e-43) {
		tmp = k * ((b * (c / k)) - (j * 27.0));
	} else if (c <= 3e-198) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (c <= 1.55e-32) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (c <= 1.02e+102) {
		tmp = t_1 + (a * (t * -4.0));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if c <= -3.5e-43:
		tmp = k * ((b * (c / k)) - (j * 27.0))
	elif c <= 3e-198:
		tmp = -4.0 * ((t * a) + (x * i))
	elif c <= 1.55e-32:
		tmp = t_1 + (-4.0 * (x * i))
	elif c <= 1.02e+102:
		tmp = t_1 + (a * (t * -4.0))
	else:
		tmp = (b * c) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (c <= -3.5e-43)
		tmp = Float64(k * Float64(Float64(b * Float64(c / k)) - Float64(j * 27.0)));
	elseif (c <= 3e-198)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (c <= 1.55e-32)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (c <= 1.02e+102)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (c <= -3.5e-43)
		tmp = k * ((b * (c / k)) - (j * 27.0));
	elseif (c <= 3e-198)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif (c <= 1.55e-32)
		tmp = t_1 + (-4.0 * (x * i));
	elseif (c <= 1.02e+102)
		tmp = t_1 + (a * (t * -4.0));
	else
		tmp = (b * c) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e-43], N[(k * N[(N[(b * N[(c / k), $MachinePrecision]), $MachinePrecision] - N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e-198], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e-32], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e+102], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.49999999999999997e-43

   1. Initial program 86.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in b around inf 44.5%

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

   6. Taylor expanded in k around -inf 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto \color{blue}{-k \cdot \left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right)} \]

      2. *-commutative 42.0%

         \[\leadsto -\color{blue}{\left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right) \cdot k} \]

      3. distribute-rgt-neg-in 42.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot c}{k} + 27 \cdot j\right) \cdot \left(-k\right)} \]

      4. +-commutative 42.0%

         \[\leadsto \color{blue}{\left(27 \cdot j + -1 \cdot \frac{b \cdot c}{k}\right)} \cdot \left(-k\right) \]

      5. mul-1-neg 42.0%

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

      6. unsub-neg 42.0%

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

      7. *-commutative 42.0%

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

      8. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

   if -3.49999999999999997e-43 < c < 3.0000000000000001e-198

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 67.8%

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

   4. Taylor expanded in j around 0 49.3%

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

      1. distribute-lft-out 49.3%

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

      2. *-commutative 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in b around 0 49.5%

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

   if 3.0000000000000001e-198 < c < 1.55000000000000005e-32

   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 96.4%

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

   5. Taylor expanded in i around inf 65.2%

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

   if 1.55000000000000005e-32 < c < 1.01999999999999999e102

   1. Initial program 90.1%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around inf 46.6%

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

      1. metadata-eval 46.6%

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

      2. distribute-lft-neg-in 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*l* 46.6%

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

      5. distribute-lft-neg-in 46.6%

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

      6. distribute-lft-neg-in 46.6%

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

      7. metadata-eval 46.6%

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

   7. Simplified 46.6%

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

   if 1.01999999999999999e102 < c

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0 68.7%

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

   4. Taylor expanded in j around 0 66.6%

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

      1. distribute-lft-out 66.6%

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

      2. *-commutative 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in t around 0 60.2%

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

      1. *-commutative 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-*l* 60.2%

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

      4. *-commutative 60.2%

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

   9. Simplified 60.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} - j \cdot 27\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-198}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(t\_1 - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -4.5e+156)
     (* t (- t_1 (* a 4.0)))
     (if (<= t 8e+77)
       (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* k (* j 27.0)))
       (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -4.5e+156) {
		tmp = t * (t_1 - (a * 4.0));
	} else if (t <= 8e+77) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-4.5d+156)) then
        tmp = t * (t_1 - (a * 4.0d0))
    else if (t <= 8d+77) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - (k * (j * 27.0d0))
    else
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -4.5e+156) {
		tmp = t * (t_1 - (a * 4.0));
	} else if (t <= 8e+77) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -4.5e+156:
		tmp = t * (t_1 - (a * 4.0))
	elif t <= 8e+77:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0))
	else:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -4.5e+156)
		tmp = Float64(t * Float64(t_1 - Float64(a * 4.0)));
	elseif (t <= 8e+77)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -4.5e+156)
		tmp = t * (t_1 - (a * 4.0));
	elseif (t <= 8e+77)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - (k * (j * 27.0));
	else
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+156], N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+77], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000031e156

   1. Initial program 82.3%

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

   3. Taylor expanded in x around 0 85.2%

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

   4. Taylor expanded in t around inf 88.6%

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

   if -4.50000000000000031e156 < t < 7.99999999999999986e77

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 82.6%

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

   if 7.99999999999999986e77 < t

   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 91.5%

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

   5. Taylor expanded in t around inf 85.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+242}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+87} \lor \neg \left(y \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -7.8e+242)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (or (<= y -1.95e+87) (not (<= y 5e-55)))
     (* x (* y (+ (* -4.0 (/ i y)) (* 18.0 (* z t)))))
     (- (* b c) (* 4.0 (+ (* t a) (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -7.8e+242) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((y <= -1.95e+87) || !(y <= 5e-55)) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-7.8d+242)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if ((y <= (-1.95d+87)) .or. (.not. (y <= 5d-55))) then
        tmp = x * (y * (((-4.0d0) * (i / y)) + (18.0d0 * (z * t))))
    else
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -7.8e+242) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((y <= -1.95e+87) || !(y <= 5e-55)) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -7.8e+242:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif (y <= -1.95e+87) or not (y <= 5e-55):
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))))
	else:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -7.8e+242)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif ((y <= -1.95e+87) || !(y <= 5e-55))
		tmp = Float64(x * Float64(y * Float64(Float64(-4.0 * Float64(i / y)) + Float64(18.0 * Float64(z * t)))));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -7.8e+242)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif ((y <= -1.95e+87) || ~((y <= 5e-55)))
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	else
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -7.8e+242], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.95e+87], N[Not[LessEqual[y, 5e-55]], $MachinePrecision]], N[(x * N[(y * N[(N[(-4.0 * N[(i / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000003e242

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 77.9%

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

   4. Taylor expanded in t around inf 82.2%

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

   if -7.8000000000000003e242 < y < -1.9500000000000001e87 or 5.0000000000000002e-55 < y

   1. Initial program 79.3%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 56.0%

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

   6. Taylor expanded in y around inf 59.5%

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

   if -1.9500000000000001e87 < y < 5.0000000000000002e-55

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in j around 0 67.7%

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

      1. distribute-lft-out 67.7%

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

      2. *-commutative 67.7%

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

   6. Simplified 67.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+242}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+87} \lor \neg \left(y \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.56e+243)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (<= y -3.4e+87)
     (* x (* y (+ (* -4.0 (/ i y)) (* 18.0 (* z t)))))
     (if (<= y 2.05e-75)
       (- (* b c) (* 4.0 (+ (* t a) (* x i))))
       (+ (* j (* k -27.0)) (* 18.0 (* (* y z) (* x t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.56e+243) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (y <= -3.4e+87) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else if (y <= 2.05e-75) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (x * 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.
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 (y <= (-1.56d+243)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (y <= (-3.4d+87)) then
        tmp = x * (y * (((-4.0d0) * (i / y)) + (18.0d0 * (z * t))))
    else if (y <= 2.05d-75) then
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    else
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * ((y * z) * (x * 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;
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 (y <= -1.56e+243) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (y <= -3.4e+87) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else if (y <= 2.05e-75) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -1.56e+243:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif y <= -3.4e+87:
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))))
	elif y <= 2.05e-75:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	else:
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (x * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.56e+243)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (y <= -3.4e+87)
		tmp = Float64(x * Float64(y * Float64(Float64(-4.0 * Float64(i / y)) + Float64(18.0 * Float64(z * t)))));
	elseif (y <= 2.05e-75)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(Float64(y * z) * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -1.56e+243)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (y <= -3.4e+87)
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	elseif (y <= 2.05e-75)
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	else
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (x * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.56e+243], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e+87], N[(x * N[(y * N[(N[(-4.0 * N[(i / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-75], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5600000000000001e243

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 77.9%

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

   4. Taylor expanded in t around inf 82.2%

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

   if -1.5600000000000001e243 < y < -3.4000000000000002e87

   1. Initial program 73.2%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 71.8%

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

   6. Taylor expanded in y around inf 77.0%

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

   if -3.4000000000000002e87 < y < 2.05000000000000001e-75

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in j around 0 67.5%

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

      1. distribute-lft-out 67.5%

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

      2. *-commutative 67.5%

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

   6. Simplified 67.5%

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

   if 2.05000000000000001e-75 < y

   1. Initial program 83.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around inf 48.9%

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

      1. associate-*r* 50.0%

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

   7. Simplified 50.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+242}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -7.2e+242)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (<= y -4.1e+86)
     (* x (* y (+ (* -4.0 (/ i y)) (* 18.0 (* z t)))))
     (if (<= y 3.2e-55)
       (- (* b c) (* 4.0 (+ (* t a) (* x i))))
       (* x (* z (+ (* -4.0 (/ i z)) (* 18.0 (* y t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -7.2e+242) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (y <= -4.1e+86) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else if (y <= 3.2e-55) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * 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.
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 (y <= (-7.2d+242)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (y <= (-4.1d+86)) then
        tmp = x * (y * (((-4.0d0) * (i / y)) + (18.0d0 * (z * t))))
    else if (y <= 3.2d-55) then
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    else
        tmp = x * (z * (((-4.0d0) * (i / z)) + (18.0d0 * (y * 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;
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 (y <= -7.2e+242) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (y <= -4.1e+86) {
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	} else if (y <= 3.2e-55) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -7.2e+242:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif y <= -4.1e+86:
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))))
	elif y <= 3.2e-55:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	else:
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -7.2e+242)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (y <= -4.1e+86)
		tmp = Float64(x * Float64(y * Float64(Float64(-4.0 * Float64(i / y)) + Float64(18.0 * Float64(z * t)))));
	elseif (y <= 3.2e-55)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(x * Float64(z * Float64(Float64(-4.0 * Float64(i / z)) + Float64(18.0 * Float64(y * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -7.2e+242)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (y <= -4.1e+86)
		tmp = x * (y * ((-4.0 * (i / y)) + (18.0 * (z * t))));
	elseif (y <= 3.2e-55)
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	else
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -7.2e+242], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e+86], N[(x * N[(y * N[(N[(-4.0 * N[(i / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-55], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(N[(-4.0 * N[(i / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.19999999999999989e242

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 77.9%

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

   4. Taylor expanded in t around inf 82.2%

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

   if -7.19999999999999989e242 < y < -4.0999999999999999e86

   1. Initial program 73.2%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 71.8%

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

   6. Taylor expanded in y around inf 77.0%

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

   if -4.0999999999999999e86 < y < 3.2000000000000001e-55

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in j around 0 67.7%

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

      1. distribute-lft-out 67.7%

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

      2. *-commutative 67.7%

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

   6. Simplified 67.7%

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

   if 3.2000000000000001e-55 < y

   1. Initial program 82.4%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x around inf 47.9%

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

   6. Taylor expanded in z around inf 51.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+242}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-4 \cdot \frac{i}{y} + 18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+24} \lor \neg \left(t \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.42e+24) (not (<= t 9.2e-15)))
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
   (- (* b c) (+ (* (* j k) 27.0) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.42e+24) || !(t <= 9.2e-15)) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = (b * c) - (((j * k) * 27.0) + (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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.42d+24)) .or. (.not. (t <= 9.2d-15))) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else
        tmp = (b * c) - (((j * k) * 27.0d0) + (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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.42e+24) || !(t <= 9.2e-15)) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = (b * c) - (((j * k) * 27.0) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.42e+24) or not (t <= 9.2e-15):
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	else:
		tmp = (b * c) - (((j * k) * 27.0) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.42e+24) || !(t <= 9.2e-15))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(Float64(j * k) * 27.0) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.42e+24) || ~((t <= 9.2e-15)))
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	else
		tmp = (b * c) - (((j * k) * 27.0) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.42e+24], N[Not[LessEqual[t, 9.2e-15]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.42e24 or 9.19999999999999961e-15 < t

   1. Initial program 84.9%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in t around inf 80.5%

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

   if -1.42e24 < t < 9.19999999999999961e-15

   1. Initial program 85.1%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around 0 76.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+24} \lor \neg \left(t \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-248}:\\ \;\;\;\;t\_2 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0))))
        (t_2 (* j (* k -27.0))))
   (if (<= x -2.15e-57)
     t_1
     (if (<= x 3.5e-248)
       (+ t_2 (* a (* t -4.0)))
       (if (<= x 8.5e-41) (+ (* b c) t_2) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -2.15e-57) {
		tmp = t_1;
	} else if (x <= 3.5e-248) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= 8.5e-41) {
		tmp = (b * c) + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-2.15d-57)) then
        tmp = t_1
    else if (x <= 3.5d-248) then
        tmp = t_2 + (a * (t * (-4.0d0)))
    else if (x <= 8.5d-41) then
        tmp = (b * c) + t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -2.15e-57) {
		tmp = t_1;
	} else if (x <= 3.5e-248) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= 8.5e-41) {
		tmp = (b * c) + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -2.15e-57:
		tmp = t_1
	elif x <= 3.5e-248:
		tmp = t_2 + (a * (t * -4.0))
	elif x <= 8.5e-41:
		tmp = (b * c) + t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -2.15e-57)
		tmp = t_1;
	elseif (x <= 3.5e-248)
		tmp = Float64(t_2 + Float64(a * Float64(t * -4.0)));
	elseif (x <= 8.5e-41)
		tmp = Float64(Float64(b * c) + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -2.15e-57)
		tmp = t_1;
	elseif (x <= 3.5e-248)
		tmp = t_2 + (a * (t * -4.0));
	elseif (x <= 8.5e-41)
		tmp = (b * c) + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e-57], t$95$1, If[LessEqual[x, 3.5e-248], N[(t$95$2 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-41], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.15000000000000011e-57 or 8.4999999999999996e-41 < x

   1. Initial program 78.5%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in x around inf 68.5%

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

      1. cancel-sign-sub-inv 68.5%

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

      2. associate-*r* 68.5%

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

      3. metadata-eval 68.5%

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

   7. Applied egg-rr 68.5%

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

   if -2.15000000000000011e-57 < x < 3.49999999999999983e-248

   1. Initial program 96.8%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around inf 69.5%

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

      1. metadata-eval 69.5%

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

      2. distribute-lft-neg-in 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*l* 69.5%

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

      5. distribute-lft-neg-in 69.5%

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

      6. distribute-lft-neg-in 69.5%

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

      7. metadata-eval 69.5%

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

   7. Simplified 69.5%

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

   if 3.49999999999999983e-248 < x < 8.4999999999999996e-41

   1. Initial program 90.3%

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

   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. Add Preprocessing

   5. Taylor expanded in b around inf 57.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-62} \lor \neg \left(x \leq 2.85 \cdot 10^{-37}\right):\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot k\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.5e-62) (not (<= x 2.85e-37)))
   (- (* b c) (* x (- (* 4.0 i) (* 18.0 (* t (* y z))))))
   (- (+ (* b c) (* -4.0 (* t a))) (* (* j k) 27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.5e-62) || !(x <= 2.85e-37)) {
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * k) * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.5d-62)) .or. (.not. (x <= 2.85d-37))) then
        tmp = (b * c) - (x * ((4.0d0 * i) - (18.0d0 * (t * (y * z)))))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((j * k) * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.5e-62) || !(x <= 2.85e-37)) {
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * k) * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.5e-62) or not (x <= 2.85e-37):
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * k) * 27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.5e-62) || !(x <= 2.85e-37))
		tmp = Float64(Float64(b * c) - Float64(x * Float64(Float64(4.0 * i) - Float64(18.0 * Float64(t * Float64(y * z))))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(j * k) * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.5e-62) || ~((x <= 2.85e-37)))
		tmp = (b * c) - (x * ((4.0 * i) - (18.0 * (t * (y * z)))));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * k) * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.5e-62], N[Not[LessEqual[x, 2.85e-37]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(x * N[(N[(4.0 * i), $MachinePrecision] - N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-62 or 2.84999999999999987e-37 < x

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 90.6%

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

   4. Taylor expanded in a around 0 81.2%

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

   5. Taylor expanded in j around 0 78.2%

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

   if -2.5000000000000001e-62 < x < 2.84999999999999987e-37

   1. Initial program 93.4%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 0 76.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-62} \lor \neg \left(x \leq 2.85 \cdot 10^{-37}\right):\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i - 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot k\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{-166}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.56 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -9.5e+128)
   (* b c)
   (if (<= (* b c) 1.7e-166)
     (* -27.0 (* j k))
     (if (<= (* b c) 1.56e+131) (* t (* a -4.0)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -9.5e+128) {
		tmp = b * c;
	} else if ((b * c) <= 1.7e-166) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.56e+131) {
		tmp = t * (a * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-9.5d+128)) then
        tmp = b * c
    else if ((b * c) <= 1.7d-166) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.56d+131) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -9.5e+128) {
		tmp = b * c;
	} else if ((b * c) <= 1.7e-166) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.56e+131) {
		tmp = t * (a * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -9.5e+128:
		tmp = b * c
	elif (b * c) <= 1.7e-166:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.56e+131:
		tmp = t * (a * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -9.5e+128)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.7e-166)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.56e+131)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -9.5e+128)
		tmp = b * c;
	elseif ((b * c) <= 1.7e-166)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.56e+131)
		tmp = t * (a * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -9.5e+128], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.7e-166], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.56e+131], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.50000000000000014e128 or 1.5600000000000001e131 < (*.f64 b c)

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 85.8%

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

   4. Taylor expanded in b around inf 55.0%

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

   if -9.50000000000000014e128 < (*.f64 b c) < 1.6999999999999999e-166

   1. Initial program 89.5%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in j around inf 25.8%

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

   if 1.6999999999999999e-166 < (*.f64 b c) < 1.5600000000000001e131

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in a around inf 30.6%

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

      1. associate-*r* 30.6%

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

      2. *-commutative 30.6%

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

   6. Simplified 30.6%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+128}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{-166}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.56 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+24} \lor \neg \left(t \leq 1.52 \cdot 10^{+63}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -4.8e+24) (not (<= t 1.52e+63)))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (- (* b c) (+ (* (* j k) 27.0) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -4.8e+24) || !(t <= 1.52e+63)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (((j * k) * 27.0) + (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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-4.8d+24)) .or. (.not. (t <= 1.52d+63))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) - (((j * k) * 27.0d0) + (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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -4.8e+24) || !(t <= 1.52e+63)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (((j * k) * 27.0) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -4.8e+24) or not (t <= 1.52e+63):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) - (((j * k) * 27.0) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -4.8e+24) || !(t <= 1.52e+63))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(Float64(j * k) * 27.0) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -4.8e+24) || ~((t <= 1.52e+63)))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) - (((j * k) * 27.0) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -4.8e+24], N[Not[LessEqual[t, 1.52e+63]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000001e24 or 1.51999999999999993e63 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 87.4%

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

   4. Taylor expanded in t around inf 76.2%

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

   if -4.8000000000000001e24 < t < 1.51999999999999993e63

   1. Initial program 85.4%

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

   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. Add Preprocessing

   5. Taylor expanded in t around 0 75.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+24} \lor \neg \left(t \leq 1.52 \cdot 10^{+63}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(j \cdot k\right) \cdot 27 + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 63.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+24} \lor \neg \left(t \leq 1.2 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.1e+24) (not (<= t 1.2e+78)))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (- (* b c) (* 4.0 (+ (* t a) (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.1e+24) || !(t <= 1.2e+78)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.1d+24)) .or. (.not. (t <= 1.2d+78))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.1e+24) || !(t <= 1.2e+78)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.1e+24) or not (t <= 1.2e+78):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.1e+24) || !(t <= 1.2e+78))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.1e+24) || ~((t <= 1.2e+78)))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.1e+24], N[Not[LessEqual[t, 1.2e+78]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000001e24 or 1.1999999999999999e78 < t

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in t around inf 76.2%

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

   if -1.10000000000000001e24 < t < 1.1999999999999999e78

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in j around 0 65.8%

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

      1. distribute-lft-out 65.8%

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

      2. *-commutative 65.8%

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

   6. Simplified 65.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+24} \lor \neg \left(t \leq 1.2 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.66 \cdot 10^{+252} \lor \neg \left(b \cdot c \leq 1.05 \cdot 10^{+216}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.66e+252) (not (<= (* b c) 1.05e+216)))
   (* b c)
   (* -4.0 (+ (* t a) (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.66e+252) || !((b * c) <= 1.05e+216)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1.66d+252)) .or. (.not. ((b * c) <= 1.05d+216))) then
        tmp = b * c
    else
        tmp = (-4.0d0) * ((t * a) + (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.66e+252) || !((b * c) <= 1.05e+216)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.66e+252) or not ((b * c) <= 1.05e+216):
		tmp = b * c
	else:
		tmp = -4.0 * ((t * a) + (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.66e+252) || !(Float64(b * c) <= 1.05e+216))
		tmp = Float64(b * c);
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.66e+252) || ~(((b * c) <= 1.05e+216)))
		tmp = b * c;
	else
		tmp = -4.0 * ((t * a) + (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.66e+252], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.05e+216]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.66e252 or 1.05000000000000001e216 < (*.f64 b c)

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0 78.7%

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

   4. Taylor expanded in b around inf 77.0%

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

   if -1.66e252 < (*.f64 b c) < 1.05000000000000001e216

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 71.6%

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

   4. Taylor expanded in j around 0 53.5%

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

      1. distribute-lft-out 53.5%

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

      2. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in b around 0 48.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.66 \cdot 10^{+252} \lor \neg \left(b \cdot c \leq 1.05 \cdot 10^{+216}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{-33} \lor \neg \left(i \leq 2.2 \cdot 10^{+92}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -2e-33) (not (<= i 2.2e+92)))
   (* -4.0 (+ (* t a) (* x i)))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -2e-33) || !(i <= 2.2e+92)) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-2d-33)) .or. (.not. (i <= 2.2d+92))) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -2e-33) || !(i <= 2.2e+92)) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -2e-33) or not (i <= 2.2e+92):
		tmp = -4.0 * ((t * a) + (x * i))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -2e-33) || !(i <= 2.2e+92))
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -2e-33) || ~((i <= 2.2e+92)))
		tmp = -4.0 * ((t * a) + (x * i));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -2e-33], N[Not[LessEqual[i, 2.2e+92]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.0000000000000001e-33 or 2.19999999999999992e92 < i

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 77.9%

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

   4. Taylor expanded in j around 0 71.5%

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

      1. distribute-lft-out 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in b around 0 66.8%

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

   if -2.0000000000000001e-33 < i < 2.19999999999999992e92

   1. Initial program 85.2%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around inf 49.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{-33} \lor \neg \left(i \leq 2.2 \cdot 10^{+92}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 34.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+185} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+215}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.3e+185) (not (<= (* b c) 8.5e+215)))
   (* b c)
   (* x (* i -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+185) || !((b * c) <= 8.5e+215)) {
		tmp = b * c;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.3d+185)) .or. (.not. ((b * c) <= 8.5d+215))) then
        tmp = b * c
    else
        tmp = x * (i * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+185) || !((b * c) <= 8.5e+215)) {
		tmp = b * c;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.3e+185) or not ((b * c) <= 8.5e+215):
		tmp = b * c
	else:
		tmp = x * (i * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.3e+185) || !(Float64(b * c) <= 8.5e+215))
		tmp = Float64(b * c);
	else
		tmp = Float64(x * Float64(i * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.3e+185) || ~(((b * c) <= 8.5e+215)))
		tmp = b * c;
	else
		tmp = x * (i * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.3e+185], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.5e+215]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.3000000000000001e185 or 8.50000000000000064e215 < (*.f64 b c)

   1. Initial program 72.6%

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

   3. Taylor expanded in x around 0 81.5%

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

   4. Taylor expanded in b around inf 72.5%

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

   if -2.3000000000000001e185 < (*.f64 b c) < 8.50000000000000064e215

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 91.7%

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

   4. Taylor expanded in i around inf 28.6%

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

      1. associate-*r* 28.6%

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

      2. *-commutative 28.6%

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

   6. Simplified 28.6%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+185} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+215}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{+128} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.6e+128) (not (<= (* b c) 2e+153)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.6e+128) || !((b * c) <= 2e+153)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.6d+128)) .or. (.not. ((b * c) <= 2d+153))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.6e+128) || !((b * c) <= 2e+153)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.6e+128) or not ((b * c) <= 2e+153):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.6e+128) || !(Float64(b * c) <= 2e+153))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.6e+128) || ~(((b * c) <= 2e+153)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.6e+128], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2e+153]], $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) < -2.6e128 or 2e153 < (*.f64 b c)

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 84.9%

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

   4. Taylor expanded in b around inf 58.6%

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

   if -2.6e128 < (*.f64 b c) < 2e153

   1. Initial program 88.6%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in j around inf 23.9%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.6 \cdot 10^{+128} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 23.9% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

3. Taylor expanded in x around 0 89.5%

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

4. Taylor expanded in b around inf 19.7%

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

Developer Target 1: 89.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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