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

Percentage Accurate: 85.7% → 89.6%

Time: 17.9s

Alternatives: 19

Speedup: 0.9×

• 50.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.6% accurate, 0.5× speedup

Math

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

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / 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):
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(c + Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(j * Float64(k * -27.0))) / 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)
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / 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_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(b * N[(c + N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $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 97.9%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.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 0 42.3%

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

   6. Taylor expanded in b around inf 57.7%

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

      1. associate--l+ 57.7%

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

      2. associate-*r/ 57.7%

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

      3. associate-*r/ 57.7%

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

      4. div-sub 57.7%

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

      5. cancel-sign-sub-inv 57.7%

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

      6. associate-*r* 57.7%

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

      7. *-commutative 57.7%

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

      8. metadata-eval 57.7%

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

      9. associate-*r* 57.7%

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

      10. *-commutative 57.7%

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

      11. associate-*r* 57.7%

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

   8. Simplified 57.7%

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

4. Final simplification 93.8%

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

Alternative 2: 88.1% accurate, 0.9× speedup

Math

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

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -inf.0

   1. Initial program 73.9%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in b around inf 87.0%

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

   6. Taylor expanded in b around inf 91.3%

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

   if -inf.0 < (*.f64 b c)

   1. Initial program 89.3%

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

   3. Simplified 90.6%

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

4. Final simplification 90.7%

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

Alternative 3: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+226}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

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) -1e+72)
   (- (* b c) (* 4.0 (* x i)))
   (if (<= (* b c) 2e-67)
     (+ (* j (* k -27.0)) (* -4.0 (* x i)))
     (if (<= (* b c) 2e+226)
       (* -4.0 (+ (* t a) (* x i)))
       (* b (+ c (* -27.0 (/ (* j k) 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) <= -1e+72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 2e-67) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+226) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= (-1d+72)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= 2d-67) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * i))
    else if ((b * c) <= 2d+226) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / 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) <= -1e+72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 2e-67) {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+226) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= -1e+72:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= 2e-67:
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i))
	elif (b * c) <= 2e+226:
		tmp = -4.0 * ((t * a) + (x * i))
	else:
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= -1e+72)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 2e-67)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 2e+226)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / 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) <= -1e+72)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= 2e-67)
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	elseif ((b * c) <= 2e+226)
		tmp = -4.0 * ((t * a) + (x * i));
	else
		tmp = b * (c + (-27.0 * ((j * k) / 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], -1e+72], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-67], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+226], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -9.99999999999999944e71

   1. Initial program 81.8%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 75.1%

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

   6. Taylor expanded in i around inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*r* 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in a around 0 68.4%

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

   if -9.99999999999999944e71 < (*.f64 b c) < 1.99999999999999989e-67

   1. Initial program 92.1%

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

   3. Simplified 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 61.0%

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

   if 1.99999999999999989e-67 < (*.f64 b c) < 1.99999999999999992e226

   1. Initial program 91.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around 0 84.0%

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

   6. Taylor expanded in i around inf 68.4%

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

      1. associate-*r* 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*r* 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in b around 0 55.2%

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

       1. cancel-sign-sub-inv 55.2%

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

       2. metadata-eval 55.2%

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

       3. distribute-lft-out 55.2%

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

   11. Simplified 55.2%

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

   if 1.99999999999999992e226 < (*.f64 b c)

   1. Initial program 78.4%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in b around inf 69.7%

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

   6. Taylor expanded in b around inf 76.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+226}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* b (+ c (* -27.0 (/ (* j k) b))))))
   (if (<= j -8.2e+56)
     t_1
     (if (<= j -8e-135)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= j 5.9e-202)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= j 1.25e-150) (* 18.0 (* t (* x (* y z)))) 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 = b * (c + (-27.0 * ((j * k) / b)));
	double tmp;
	if (j <= -8.2e+56) {
		tmp = t_1;
	} else if (j <= -8e-135) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 5.9e-202) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 1.25e-150) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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 = b * (c + ((-27.0d0) * ((j * k) / b)))
    if (j <= (-8.2d+56)) then
        tmp = t_1
    else if (j <= (-8d-135)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (j <= 5.9d-202) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (j <= 1.25d-150) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    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 = b * (c + (-27.0 * ((j * k) / b)));
	double tmp;
	if (j <= -8.2e+56) {
		tmp = t_1;
	} else if (j <= -8e-135) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 5.9e-202) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 1.25e-150) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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 = b * (c + (-27.0 * ((j * k) / b)))
	tmp = 0
	if j <= -8.2e+56:
		tmp = t_1
	elif j <= -8e-135:
		tmp = (b * c) + (-4.0 * (t * a))
	elif j <= 5.9e-202:
		tmp = (b * c) - (4.0 * (x * i))
	elif j <= 1.25e-150:
		tmp = 18.0 * (t * (x * (y * z)))
	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(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))))
	tmp = 0.0
	if (j <= -8.2e+56)
		tmp = t_1;
	elseif (j <= -8e-135)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= 5.9e-202)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (j <= 1.25e-150)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	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 = b * (c + (-27.0 * ((j * k) / b)));
	tmp = 0.0;
	if (j <= -8.2e+56)
		tmp = t_1;
	elseif (j <= -8e-135)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (j <= 5.9e-202)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (j <= 1.25e-150)
		tmp = 18.0 * (t * (x * (y * z)));
	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[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.2e+56], t$95$1, If[LessEqual[j, -8e-135], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.9e-202], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-150], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.2000000000000007e56 or 1.24999999999999997e-150 < j

   1. Initial program 85.5%

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

   3. Simplified 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 62.9%

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

   6. Taylor expanded in b around inf 64.2%

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

   if -8.2000000000000007e56 < j < -8.0000000000000003e-135

   1. Initial program 95.5%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around 0 60.4%

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

   6. Taylor expanded in j around 0 52.2%

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

   if -8.0000000000000003e-135 < j < 5.89999999999999999e-202

   1. Initial program 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around 0 77.6%

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

   6. Taylor expanded in i around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*r* 74.0%

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

   8. Simplified 74.0%

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

   9. Taylor expanded in a around 0 47.5%

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

   if 5.89999999999999999e-202 < j < 1.24999999999999997e-150

   1. Initial program 90.8%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 51.8%

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

   6. Taylor expanded in t around inf 51.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (* t (+ (* a -4.0) (* 18.0 (* x (* y z)))))))
   (if (<= t -7.2e+253)
     t_2
     (if (<= t -1.8e-84)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= t 1.15e+78) (- (* b c) (+ (* 4.0 (* x i)) t_1)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -7.2e+253) {
		tmp = t_2;
	} else if (t <= -1.8e-84) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 1.15e+78) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    if (t <= (-7.2d+253)) then
        tmp = t_2
    else if (t <= (-1.8d-84)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (t <= 1.15d+78) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -7.2e+253) {
		tmp = t_2;
	} else if (t <= -1.8e-84) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 1.15e+78) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	tmp = 0
	if t <= -7.2e+253:
		tmp = t_2
	elif t <= -1.8e-84:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif t <= 1.15e+78:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -7.2e+253)
		tmp = t_2;
	elseif (t <= -1.8e-84)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (t <= 1.15e+78)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	tmp = 0.0;
	if (t <= -7.2e+253)
		tmp = t_2;
	elseif (t <= -1.8e-84)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (t <= 1.15e+78)
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+253], t$95$2, If[LessEqual[t, -1.8e-84], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.15e+78], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000001e253 or 1.1500000000000001e78 < t

   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 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 t around inf 84.8%

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

   6. Taylor expanded in t around inf 81.8%

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

   if -7.2000000000000001e253 < t < -1.80000000000000002e-84

   1. Initial program 95.6%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 73.8%

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

   if -1.80000000000000002e-84 < t < 1.1500000000000001e78

   1. Initial program 88.1%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around 0 84.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -1 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.36 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-27 \cdot \left(j \cdot \frac{k}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= k -1e+40)
     t_1
     (if (<= k 1.36e+82)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= k 2.1e+124)
         t_1
         (if (<= k 1.35e+217)
           (* -4.0 (+ (* t a) (* x i)))
           (* b (* -27.0 (* j (/ k 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 t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -1e+40) {
		tmp = t_1;
	} else if (k <= 1.36e+82) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (k <= 2.1e+124) {
		tmp = t_1;
	} else if (k <= 1.35e+217) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = b * (-27.0 * (j * (k / 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) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (k <= (-1d+40)) then
        tmp = t_1
    else if (k <= 1.36d+82) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (k <= 2.1d+124) then
        tmp = t_1
    else if (k <= 1.35d+217) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else
        tmp = b * ((-27.0d0) * (j * (k / 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 t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -1e+40) {
		tmp = t_1;
	} else if (k <= 1.36e+82) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (k <= 2.1e+124) {
		tmp = t_1;
	} else if (k <= 1.35e+217) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = b * (-27.0 * (j * (k / 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):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if k <= -1e+40:
		tmp = t_1
	elif k <= 1.36e+82:
		tmp = (b * c) + (-4.0 * (t * a))
	elif k <= 2.1e+124:
		tmp = t_1
	elif k <= 1.35e+217:
		tmp = -4.0 * ((t * a) + (x * i))
	else:
		tmp = b * (-27.0 * (j * (k / 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)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -1e+40)
		tmp = t_1;
	elseif (k <= 1.36e+82)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (k <= 2.1e+124)
		tmp = t_1;
	elseif (k <= 1.35e+217)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	else
		tmp = Float64(b * Float64(-27.0 * Float64(j * Float64(k / 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)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -1e+40)
		tmp = t_1;
	elseif (k <= 1.36e+82)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (k <= 2.1e+124)
		tmp = t_1;
	elseif (k <= 1.35e+217)
		tmp = -4.0 * ((t * a) + (x * i));
	else
		tmp = b * (-27.0 * (j * (k / 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_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1e+40], t$95$1, If[LessEqual[k, 1.36e+82], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+124], t$95$1, If[LessEqual[k, 1.35e+217], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(-27.0 * N[(j * N[(k / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.00000000000000003e40 or 1.36000000000000001e82 < k < 2.10000000000000011e124

   1. Initial program 85.8%

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

   3. Simplified 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 j around inf 51.2%

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

   if -1.00000000000000003e40 < k < 1.36000000000000001e82

   1. Initial program 90.0%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around 0 63.4%

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

   6. Taylor expanded in j around 0 51.0%

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

   if 2.10000000000000011e124 < k < 1.35000000000000001e217

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in i around inf 69.3%

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

      1. associate-*r* 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-*r* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in b around 0 57.4%

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

       1. cancel-sign-sub-inv 57.4%

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

       2. metadata-eval 57.4%

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

       3. distribute-lft-out 57.4%

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

   11. Simplified 57.4%

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

   if 1.35000000000000001e217 < k

   1. Initial program 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in b around inf 56.7%

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

   6. Taylor expanded in b around inf 72.3%

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

   7. Taylor expanded in c around 0 61.9%

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

      1. associate-*r/ 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1 \cdot 10^{+40}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.36 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+217}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-27 \cdot \left(j \cdot \frac{k}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -58 \lor \neg \left(t \leq 8.6 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

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 -58.0) (not (<= t 8.6e+72)))
   (+ (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))) (* j (* k -27.0)))
   (- (* b c) (+ (* 4.0 (* x i)) (* 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 ((t <= -58.0) || !(t <= 8.6e+72)) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (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 ((t <= (-58.0d0)) .or. (.not. (t <= 8.6d+72))) then
        tmp = (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (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 ((t <= -58.0) || !(t <= 8.6e+72)) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (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 (t <= -58.0) or not (t <= 8.6e+72):
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (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 ((t <= -58.0) || !(t <= 8.6e+72))
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + 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 ((t <= -58.0) || ~((t <= 8.6e+72)))
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (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[t, -58.0], N[Not[LessEqual[t, 8.6e+72]], $MachinePrecision]], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -58 or 8.6000000000000003e72 < t

   1. Initial program 86.5%

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

   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 81.5%

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

   if -58 < t < 8.6000000000000003e72

   1. Initial program 89.1%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t around 0 83.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -58 \lor \neg \left(t \leq 8.6 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -49:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* a -4.0) (* 18.0 (* x (* y z)))))))
   (if (<= t -49.0)
     t_1
     (if (<= t 4.6e-156)
       (* b (+ c (* -27.0 (/ (* j k) b))))
       (if (<= t 1.25e+73) (- (* b c) (* 4.0 (* x i))) 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 * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -49.0) {
		tmp = t_1;
	} else if (t <= 4.6e-156) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= 1.25e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} 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 * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    if (t <= (-49.0d0)) then
        tmp = t_1
    else if (t <= 4.6d-156) then
        tmp = b * (c + ((-27.0d0) * ((j * k) / b)))
    else if (t <= 1.25d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    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 * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -49.0) {
		tmp = t_1;
	} else if (t <= 4.6e-156) {
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	} else if (t <= 1.25e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} 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 * ((a * -4.0) + (18.0 * (x * (y * z))))
	tmp = 0
	if t <= -49.0:
		tmp = t_1
	elif t <= 4.6e-156:
		tmp = b * (c + (-27.0 * ((j * k) / b)))
	elif t <= 1.25e+73:
		tmp = (b * c) - (4.0 * (x * i))
	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(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -49.0)
		tmp = t_1;
	elseif (t <= 4.6e-156)
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / b))));
	elseif (t <= 1.25e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	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 * ((a * -4.0) + (18.0 * (x * (y * z))));
	tmp = 0.0;
	if (t <= -49.0)
		tmp = t_1;
	elseif (t <= 4.6e-156)
		tmp = b * (c + (-27.0 * ((j * k) / b)));
	elseif (t <= 1.25e+73)
		tmp = (b * c) - (4.0 * (x * i));
	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[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -49.0], t$95$1, If[LessEqual[t, 4.6e-156], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -49 or 1.24999999999999994e73 < t

   1. Initial program 86.5%

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

   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 81.5%

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

   6. Taylor expanded in t around inf 71.2%

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

   if -49 < t < 4.5999999999999999e-156

   1. Initial program 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in b around inf 68.1%

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

   6. Taylor expanded in b around inf 70.3%

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

   if 4.5999999999999999e-156 < t < 1.24999999999999994e73

   1. Initial program 92.2%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around 0 90.2%

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

   6. Taylor expanded in i around inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in a around 0 66.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -49:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-156}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.14 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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) -4.5e+68)
   (* b c)
   (if (<= (* b c) 1.65e-65)
     (* j (* k -27.0))
     (if (<= (* b c) 1.14e+226) (* 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) <= -4.5e+68) {
		tmp = b * c;
	} else if ((b * c) <= 1.65e-65) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.14e+226) {
		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) <= (-4.5d+68)) then
        tmp = b * c
    else if ((b * c) <= 1.65d-65) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 1.14d+226) 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) <= -4.5e+68) {
		tmp = b * c;
	} else if ((b * c) <= 1.65e-65) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.14e+226) {
		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) <= -4.5e+68:
		tmp = b * c
	elif (b * c) <= 1.65e-65:
		tmp = j * (k * -27.0)
	elif (b * c) <= 1.14e+226:
		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) <= -4.5e+68)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.65e-65)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 1.14e+226)
		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) <= -4.5e+68)
		tmp = b * c;
	elseif ((b * c) <= 1.65e-65)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 1.14e+226)
		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], -4.5e+68], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-65], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.14e+226], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.5000000000000003e68 or 1.14000000000000003e226 < (*.f64 b c)

   1. Initial program 80.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 77.4%

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

   6. Taylor expanded in b around inf 58.6%

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

   if -4.5000000000000003e68 < (*.f64 b c) < 1.6500000000000001e-65

   1. Initial program 92.1%

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

   3. Simplified 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 j around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. *-commutative 41.3%

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

      3. metadata-eval 41.3%

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

      4. distribute-rgt-neg-in 41.3%

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

      5. *-commutative 41.3%

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

      6. distribute-rgt-neg-in 41.3%

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

      7. metadata-eval 41.3%

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

      8. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   8. Taylor expanded in k around 0 41.3%

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

      1. *-commutative 41.3%

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

      2. associate-*r* 41.3%

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

   10. Simplified 41.3%

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

   if 1.6500000000000001e-65 < (*.f64 b c) < 1.14000000000000003e226

   1. Initial program 91.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around 0 84.0%

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

   6. Taylor expanded in a around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. *-commutative 41.1%

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

   8. Simplified 41.1%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.14 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+71}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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) -1.15e+71)
   (* b c)
   (if (<= (* b c) 7e-67)
     (* k (* j -27.0))
     (if (<= (* b c) 1.25e+226) (* 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) <= -1.15e+71) {
		tmp = b * c;
	} else if ((b * c) <= 7e-67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.25e+226) {
		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) <= (-1.15d+71)) then
        tmp = b * c
    else if ((b * c) <= 7d-67) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.25d+226) 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) <= -1.15e+71) {
		tmp = b * c;
	} else if ((b * c) <= 7e-67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.25e+226) {
		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) <= -1.15e+71:
		tmp = b * c
	elif (b * c) <= 7e-67:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.25e+226:
		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) <= -1.15e+71)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 7e-67)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.25e+226)
		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) <= -1.15e+71)
		tmp = b * c;
	elseif ((b * c) <= 7e-67)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.25e+226)
		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], -1.15e+71], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7e-67], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.25e+226], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.1500000000000001e71 or 1.2500000000000001e226 < (*.f64 b c)

   1. Initial program 80.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 77.4%

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

   6. Taylor expanded in b around inf 58.6%

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

   if -1.1500000000000001e71 < (*.f64 b c) < 7.0000000000000001e-67

   1. Initial program 92.1%

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

   3. Simplified 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 j around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. *-commutative 41.3%

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

      3. metadata-eval 41.3%

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

      4. distribute-rgt-neg-in 41.3%

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

      5. *-commutative 41.3%

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

      6. distribute-rgt-neg-in 41.3%

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

      7. metadata-eval 41.3%

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

      8. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   if 7.0000000000000001e-67 < (*.f64 b c) < 1.2500000000000001e226

   1. Initial program 91.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around 0 84.0%

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

   6. Taylor expanded in a around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. *-commutative 41.1%

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

   8. Simplified 41.1%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+71}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.15 \cdot 10^{+162}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= z 3.15e+162)
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
   (+ (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))) (* 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 (z <= 3.15e+162) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (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 (z <= 3.15d+162) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))) + (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 (z <= 3.15e+162) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (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 z <= 3.15e+162:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (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 (z <= 3.15e+162)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))) + 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 (z <= 3.15e+162)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (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[LessEqual[z, 3.15e+162], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.15e162

   1. Initial program 89.9%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 83.6%

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

   if 3.15e162 < z

   1. Initial program 73.3%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in t around inf 77.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.15 \cdot 10^{+162}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+55} \lor \neg \left(t \leq 1.05 \cdot 10^{+79}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

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 -1.7e+55) (not (<= t 1.05e+79)))
   (* t (+ (* a -4.0) (* 18.0 (* x (* y z)))))
   (- (* b c) (+ (* 4.0 (* x i)) (* 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 ((t <= -1.7e+55) || !(t <= 1.05e+79)) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (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 ((t <= (-1.7d+55)) .or. (.not. (t <= 1.05d+79))) then
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (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 ((t <= -1.7e+55) || !(t <= 1.05e+79)) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (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 (t <= -1.7e+55) or not (t <= 1.05e+79):
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (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 ((t <= -1.7e+55) || !(t <= 1.05e+79))
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + 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 ((t <= -1.7e+55) || ~((t <= 1.05e+79)))
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (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[t, -1.7e+55], N[Not[LessEqual[t, 1.05e+79]], $MachinePrecision]], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e55 or 1.05000000000000004e79 < t

   1. Initial program 84.6%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in t around inf 82.8%

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

   6. Taylor expanded in t around inf 75.0%

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

   if -1.6999999999999999e55 < t < 1.05000000000000004e79

   1. Initial program 90.0%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around 0 81.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+55} \lor \neg \left(t \leq 1.05 \cdot 10^{+79}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(c + \frac{t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)}{b}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.7e-231)
   (* b (+ c (/ (+ (* t (* a -4.0)) (* j (* k -27.0))) b)))
   (if (<= t 1.9e+76)
     (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.7e-231) {
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / b));
	} else if (t <= 1.9e+76) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.7d-231)) then
        tmp = b * (c + (((t * (a * (-4.0d0))) + (j * (k * (-27.0d0)))) / b))
    else if (t <= 1.9d+76) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.7e-231) {
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / b));
	} else if (t <= 1.9e+76) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.7e-231:
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / b))
	elif t <= 1.9e+76:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.7e-231)
		tmp = Float64(b * Float64(c + Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(j * Float64(k * -27.0))) / b)));
	elseif (t <= 1.9e+76)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.7e-231)
		tmp = b * (c + (((t * (a * -4.0)) + (j * (k * -27.0))) / b));
	elseif (t <= 1.9e+76)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.7e-231], N[(b * N[(c + N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+76], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e-231

   1. Initial program 87.7%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around 0 69.4%

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

   6. Taylor expanded in b around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. div-sub 72.3%

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

      5. cancel-sign-sub-inv 72.3%

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

      6. associate-*r* 72.3%

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

      7. *-commutative 72.3%

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

      8. metadata-eval 72.3%

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

      9. associate-*r* 72.3%

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

      10. *-commutative 72.3%

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

      11. associate-*r* 72.3%

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

   8. Simplified 72.3%

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

   if -1.7e-231 < t < 1.90000000000000012e76

   1. Initial program 90.4%

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

   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 t around 0 85.7%

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

   if 1.90000000000000012e76 < t

   1. Initial program 82.9%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 87.5%

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

   6. Taylor expanded in t around inf 83.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(c + \frac{t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)}{b}\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+226}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \end{array} \]

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) -1e+72)
   (- (* b c) (* 4.0 (* x i)))
   (if (<= (* b c) 2e+226)
     (+ (* -4.0 (* t a)) (* j (* k -27.0)))
     (* b (+ c (* -27.0 (/ (* j k) 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) <= -1e+72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 2e+226) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= (-1d+72)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= 2d+226) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else
        tmp = b * (c + ((-27.0d0) * ((j * k) / 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) <= -1e+72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 2e+226) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else {
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= -1e+72:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= 2e+226:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	else:
		tmp = b * (c + (-27.0 * ((j * k) / 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) <= -1e+72)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 2e+226)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(Float64(j * k) / 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) <= -1e+72)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= 2e+226)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	else
		tmp = b * (c + (-27.0 * ((j * k) / 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], -1e+72], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+226], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.99999999999999944e71

   1. Initial program 81.8%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 75.1%

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

   6. Taylor expanded in i around inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*r* 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in a around 0 68.4%

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

   if -9.99999999999999944e71 < (*.f64 b c) < 1.99999999999999992e226

   1. Initial program 92.1%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 1.99999999999999992e226 < (*.f64 b c)

   1. Initial program 78.4%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in b around inf 69.7%

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

   6. Taylor expanded in b around inf 76.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+226}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+110} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+237}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

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) -1e+110) (not (<= (* b c) 5e+237)))
   (* 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) <= -1e+110) || !((b * c) <= 5e+237)) {
		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) <= (-1d+110)) .or. (.not. ((b * c) <= 5d+237))) 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) <= -1e+110) || !((b * c) <= 5e+237)) {
		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) <= -1e+110) or not ((b * c) <= 5e+237):
		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) <= -1e+110) || !(Float64(b * c) <= 5e+237))
		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) <= -1e+110) || ~(((b * c) <= 5e+237)))
		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], -1e+110], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5e+237]], $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) < -1e110 or 5.0000000000000002e237 < (*.f64 b c)

   1. Initial program 78.4%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 75.9%

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

   6. Taylor expanded in b around inf 62.6%

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

   if -1e110 < (*.f64 b c) < 5.0000000000000002e237

   1. Initial program 92.1%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 83.1%

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

   6. Taylor expanded in i around inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. *-commutative 55.1%

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

      3. associate-*r* 55.1%

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

   8. Simplified 55.1%

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

   9. Taylor expanded in b around 0 48.8%

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

       1. cancel-sign-sub-inv 48.8%

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

       2. metadata-eval 48.8%

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

       3. distribute-lft-out 48.8%

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

   11. Simplified 48.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+110} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+237}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+68} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+270}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4.8e+68) (not (<= (* b c) 8.5e+270)))
   (* b c)
   (* k (* j -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.8e+68) || !((b * c) <= 8.5e+270)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-4.8d+68)) .or. (.not. ((b * c) <= 8.5d+270))) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.8e+68) || !((b * c) <= 8.5e+270)) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -4.8e+68) or not ((b * c) <= 8.5e+270):
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -4.8e+68) || !(Float64(b * c) <= 8.5e+270))
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -4.8e+68) || ~(((b * c) <= 8.5e+270)))
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4.8e+68], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.5e+270]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.80000000000000016e68 or 8.50000000000000063e270 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around 0 76.5%

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

   6. Taylor expanded in b around inf 61.5%

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

   if -4.80000000000000016e68 < (*.f64 b c) < 8.50000000000000063e270

   1. Initial program 91.9%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.9%

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

      2. *-commutative 35.9%

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

      3. metadata-eval 35.9%

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

      4. distribute-rgt-neg-in 35.9%

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

      5. *-commutative 35.9%

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

      6. distribute-rgt-neg-in 35.9%

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

      7. metadata-eval 35.9%

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

      8. *-commutative 35.9%

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

   7. Simplified 35.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+68} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+270}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+71} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+270}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -2.9e+71) (not (<= (* b c) 8.5e+270)))
   (* 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) <= -2.9e+71) || !((b * c) <= 8.5e+270)) {
		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) <= (-2.9d+71)) .or. (.not. ((b * c) <= 8.5d+270))) 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) <= -2.9e+71) || !((b * c) <= 8.5e+270)) {
		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) <= -2.9e+71) or not ((b * c) <= 8.5e+270):
		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) <= -2.9e+71) || !(Float64(b * c) <= 8.5e+270))
		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) <= -2.9e+71) || ~(((b * c) <= 8.5e+270)))
		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], -2.9e+71], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.5e+270]], $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) < -2.90000000000000007e71 or 8.50000000000000063e270 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around 0 76.5%

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

   6. Taylor expanded in b around inf 61.5%

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

   if -2.90000000000000007e71 < (*.f64 b c) < 8.50000000000000063e270

   1. Initial program 91.9%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in j around inf 35.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+71} \lor \neg \left(b \cdot c \leq 8.5 \cdot 10^{+270}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+173}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

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 (<= t -4.3e+173)
   (+ (* b c) (* -4.0 (* t a)))
   (if (<= t 8.5e+26)
     (+ (* b c) (* j (* k -27.0)))
     (* -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 <= -4.3e+173) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t <= 8.5e+26) {
		tmp = (b * c) + (j * (k * -27.0));
	} 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 (t <= (-4.3d+173)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t <= 8.5d+26) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    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 (t <= -4.3e+173) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t <= 8.5e+26) {
		tmp = (b * c) + (j * (k * -27.0));
	} 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 t <= -4.3e+173:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t <= 8.5e+26:
		tmp = (b * c) + (j * (k * -27.0))
	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 (t <= -4.3e+173)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t <= 8.5e+26)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	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 (t <= -4.3e+173)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t <= 8.5e+26)
		tmp = (b * c) + (j * (k * -27.0));
	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[LessEqual[t, -4.3e+173], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+26], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.30000000000000025e173

   1. Initial program 82.8%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around 0 67.0%

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

   6. Taylor expanded in j around 0 61.1%

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

   if -4.30000000000000025e173 < t < 8.5e26

   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 90.9%

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

   5. Taylor expanded in b around inf 60.8%

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

   if 8.5e26 < t

   1. Initial program 84.5%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around 0 71.2%

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

   6. Taylor expanded in i around inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*r* 66.3%

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

   8. Simplified 66.3%

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

   9. Taylor expanded in b around 0 55.9%

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

       1. cancel-sign-sub-inv 55.9%

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

       2. metadata-eval 55.9%

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

       3. distribute-lft-out 55.9%

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

   11. Simplified 55.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+173}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.0% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Simplified 88.7%

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

5. Taylor expanded in y around 0 80.9%

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

6. Taylor expanded in b around inf 24.7%

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

Developer Target 1: 89.7% 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 2024138 
(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)))