Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.4% → 40.0%

Time: 1.8min

Alternatives: 37

Speedup: 3.5×

• 88.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (+
  (-
   (+
    (+
     (-
      (* (- (* x y) (* z t)) (- (* a b) (* c i)))
      (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
     (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
    (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
   (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
  (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 30.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (+
  (-
   (+
    (+
     (-
      (* (- (* x y) (* z t)) (- (* a b) (* c i)))
      (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
     (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
    (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
   (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
  (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 40.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := a \cdot b - c \cdot i\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := y5 \cdot \left(i \cdot t_1 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot t_5\right)\right)\\ t_7 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t_5 - t_1 \cdot b\right) + c \cdot t_7\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_2 + y2 \cdot t_4\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -4.7 \cdot 10^{-117}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_4 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-288}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_3\right) + y4 \cdot t_7\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 30:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t_3 + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{+33} \lor \neg \left(y4 \leq 4.8 \cdot 10^{+120}\right):\\ \;\;\;\;\left(c \cdot y4\right) \cdot t_7\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_2\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (* y5 (+ (* i t_1) (- (* a (- (* t y2) (* y y3))) (* y0 t_5)))))
        (t_7 (- (* y y3) (* t y2))))
   (if (<= y4 -2.4e+109)
     (* y4 (+ (- (* y1 t_5) (* t_1 b)) (* c t_7)))
     (if (<= y4 -1.5e-9)
       (* x (+ (+ (* y t_2) (* y2 t_4)) (* j (- (* i y1) (* b y0)))))
       (if (<= y4 -4.7e-117)
         (*
          y2
          (+
           (+ (* x t_4) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y4 -9e-288)
           t_6
           (if (<= y4 9.6e-147)
             (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_3)) (* y4 t_7)))
             (if (<= y4 6.5e-43)
               t_6
               (if (<= y4 30.0)
                 (*
                  y1
                  (-
                   (* i (- (* x j) (* z k)))
                   (+ (* a t_3) (* y4 (- (* j y3) (* k y2))))))
                 (if (or (<= y4 4.4e+33) (not (<= y4 4.8e+120)))
                   (* (* c y4) t_7)
                   (*
                    y
                    (+
                     (+ (* k (- (* i y5) (* b y4))) (* x t_2))
                     (* y3 (- (* c y4) (* a y5)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * b) - (c * i);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_5)));
	double t_7 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -2.4e+109) {
		tmp = y4 * (((y1 * t_5) - (t_1 * b)) + (c * t_7));
	} else if (y4 <= -1.5e-9) {
		tmp = x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -4.7e-117) {
		tmp = y2 * (((x * t_4) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -9e-288) {
		tmp = t_6;
	} else if (y4 <= 9.6e-147) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_7));
	} else if (y4 <= 6.5e-43) {
		tmp = t_6;
	} else if (y4 <= 30.0) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * ((j * y3) - (k * y2)))));
	} else if ((y4 <= 4.4e+33) || !(y4 <= 4.8e+120)) {
		tmp = (c * y4) * t_7;
	} else {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (a * b) - (c * i)
    t_3 = (x * y2) - (z * y3)
    t_4 = (c * y0) - (a * y1)
    t_5 = (k * y2) - (j * y3)
    t_6 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_5)))
    t_7 = (y * y3) - (t * y2)
    if (y4 <= (-2.4d+109)) then
        tmp = y4 * (((y1 * t_5) - (t_1 * b)) + (c * t_7))
    else if (y4 <= (-1.5d-9)) then
        tmp = x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
    else if (y4 <= (-4.7d-117)) then
        tmp = y2 * (((x * t_4) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y4 <= (-9d-288)) then
        tmp = t_6
    else if (y4 <= 9.6d-147) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_7))
    else if (y4 <= 6.5d-43) then
        tmp = t_6
    else if (y4 <= 30.0d0) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * ((j * y3) - (k * y2)))))
    else if ((y4 <= 4.4d+33) .or. (.not. (y4 <= 4.8d+120))) then
        tmp = (c * y4) * t_7
    else
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * b) - (c * i);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_5)));
	double t_7 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -2.4e+109) {
		tmp = y4 * (((y1 * t_5) - (t_1 * b)) + (c * t_7));
	} else if (y4 <= -1.5e-9) {
		tmp = x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -4.7e-117) {
		tmp = y2 * (((x * t_4) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -9e-288) {
		tmp = t_6;
	} else if (y4 <= 9.6e-147) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_7));
	} else if (y4 <= 6.5e-43) {
		tmp = t_6;
	} else if (y4 <= 30.0) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * ((j * y3) - (k * y2)))));
	} else if ((y4 <= 4.4e+33) || !(y4 <= 4.8e+120)) {
		tmp = (c * y4) * t_7;
	} else {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (a * b) - (c * i)
	t_3 = (x * y2) - (z * y3)
	t_4 = (c * y0) - (a * y1)
	t_5 = (k * y2) - (j * y3)
	t_6 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_5)))
	t_7 = (y * y3) - (t * y2)
	tmp = 0
	if y4 <= -2.4e+109:
		tmp = y4 * (((y1 * t_5) - (t_1 * b)) + (c * t_7))
	elif y4 <= -1.5e-9:
		tmp = x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))))
	elif y4 <= -4.7e-117:
		tmp = y2 * (((x * t_4) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y4 <= -9e-288:
		tmp = t_6
	elif y4 <= 9.6e-147:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_7))
	elif y4 <= 6.5e-43:
		tmp = t_6
	elif y4 <= 30.0:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * ((j * y3) - (k * y2)))))
	elif (y4 <= 4.4e+33) or not (y4 <= 4.8e+120):
		tmp = (c * y4) * t_7
	else:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(y5 * Float64(Float64(i * t_1) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y0 * t_5))))
	t_7 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (y4 <= -2.4e+109)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_5) - Float64(t_1 * b)) + Float64(c * t_7)));
	elseif (y4 <= -1.5e-9)
		tmp = Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * t_4)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= -4.7e-117)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_4) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y4 <= -9e-288)
		tmp = t_6;
	elseif (y4 <= 9.6e-147)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_3)) + Float64(y4 * t_7)));
	elseif (y4 <= 6.5e-43)
		tmp = t_6;
	elseif (y4 <= 30.0)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_3) + Float64(y4 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif ((y4 <= 4.4e+33) || !(y4 <= 4.8e+120))
		tmp = Float64(Float64(c * y4) * t_7);
	else
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_2)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (a * b) - (c * i);
	t_3 = (x * y2) - (z * y3);
	t_4 = (c * y0) - (a * y1);
	t_5 = (k * y2) - (j * y3);
	t_6 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_5)));
	t_7 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (y4 <= -2.4e+109)
		tmp = y4 * (((y1 * t_5) - (t_1 * b)) + (c * t_7));
	elseif (y4 <= -1.5e-9)
		tmp = x * (((y * t_2) + (y2 * t_4)) + (j * ((i * y1) - (b * y0))));
	elseif (y4 <= -4.7e-117)
		tmp = y2 * (((x * t_4) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y4 <= -9e-288)
		tmp = t_6;
	elseif (y4 <= 9.6e-147)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * t_7));
	elseif (y4 <= 6.5e-43)
		tmp = t_6;
	elseif (y4 <= 30.0)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * ((j * y3) - (k * y2)))));
	elseif ((y4 <= 4.4e+33) || ~((y4 <= 4.8e+120)))
		tmp = (c * y4) * t_7;
	else
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y5 * N[(N[(i * t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.4e+109], N[(y4 * N[(N[(N[(y1 * t$95$5), $MachinePrecision] - N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.5e-9], N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.7e-117], N[(y2 * N[(N[(N[(x * t$95$4), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9e-288], t$95$6, If[LessEqual[y4, 9.6e-147], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-43], t$95$6, If[LessEqual[y4, 30.0], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y4, 4.4e+33], N[Not[LessEqual[y4, 4.8e+120]], $MachinePrecision]], N[(N[(c * y4), $MachinePrecision] * t$95$7), $MachinePrecision], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -2.39999999999999987e109

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 67.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -2.39999999999999987e109 < y4 < -1.49999999999999999e-9

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -1.49999999999999999e-9 < y4 < -4.70000000000000009e-117

   1. Initial program 4.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 4.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 4.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 56.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   if -4.70000000000000009e-117 < y4 < -9.0000000000000003e-288 or 9.59999999999999994e-147 < y4 < 6.50000000000000001e-43

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 60.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.2%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 60.2%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 60.2%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if -9.0000000000000003e-288 < y4 < 9.59999999999999994e-147

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 66.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.5%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 6.50000000000000001e-43 < y4 < 30

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y1 around inf 64.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(a \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + \color{blue}{\left(-a \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 64.1%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(-a \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(-a \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - \left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   if 30 < y4 < 4.39999999999999988e33 or 4.80000000000000002e120 < y4

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 59.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.4%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   7. Simplified 57.4%

      \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   if 4.39999999999999988e33 < y4 < 4.80000000000000002e120

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 77.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.0%

         \[\leadsto y \cdot \left(\left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      2. mul-1-neg 77.0%

         \[\leadsto y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

   6. Simplified 77.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.4 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -4.7 \cdot 10^{-117}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-288}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 30:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{+33} \lor \neg \left(y4 \leq 4.8 \cdot 10^{+120}\right):\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \]

Alternative 2: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := \left(\left(\left(\left(t_1 \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_1\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2
         (+
          (+
           (+
            (+
             (+
              (* t_1 (- (* x y) (* z t)))
              (* (- (* b y0) (* i y1)) (- (* z k) (* x j))))
             (* (- (* c y0) (* a y1)) (- (* x y2) (* z y3))))
            (* (- (* b y4) (* i y5)) (- (* t j) (* y k))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))
   (if (<= t_2 INFINITY)
     t_2
     (*
      y
      (+
       (+ (* k (- (* i y5) (* b y4))) (* x t_1))
       (* y3 (- (* c y4) (* a y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (((((t_1 * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_1)) + (y3 * ((c * y4) - (a * y5))));
	}
	return tmp;
}

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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (((((t_1 * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_1)) + (y3 * ((c * y4) - (a * y5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * b) - (c * i)
	t_2 = (((((t_1 * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_1)) + (y3 * ((c * y4) - (a * y5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(t_1 * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(Float64(Float64(c * y0) - Float64(a * y1)) * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_1)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * b) - (c * i);
	t_2 = (((((t_1 * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_1)) + (y3 * ((c * y4) - (a * y5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(t$95$1 * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 a b) (*.f64 c i))) (*.f64 (-.f64 (*.f64 x j) (*.f64 z k)) (-.f64 (*.f64 y0 b) (*.f64 y1 i)))) (*.f64 (-.f64 (*.f64 x y2) (*.f64 z y3)) (-.f64 (*.f64 y0 c) (*.f64 y1 a)))) (*.f64 (-.f64 (*.f64 t j) (*.f64 y k)) (-.f64 (*.f64 y4 b) (*.f64 y5 i)))) (*.f64 (-.f64 (*.f64 t y2) (*.f64 y y3)) (-.f64 (*.f64 y4 c) (*.f64 y5 a)))) (*.f64 (-.f64 (*.f64 k y2) (*.f64 j y3)) (-.f64 (*.f64 y4 y1) (*.f64 y5 y0)))) < +inf.0

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if +inf.0 < (+.f64 (-.f64 (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 a b) (*.f64 c i))) (*.f64 (-.f64 (*.f64 x j) (*.f64 z k)) (-.f64 (*.f64 y0 b) (*.f64 y1 i)))) (*.f64 (-.f64 (*.f64 x y2) (*.f64 z y3)) (-.f64 (*.f64 y0 c) (*.f64 y1 a)))) (*.f64 (-.f64 (*.f64 t j) (*.f64 y k)) (-.f64 (*.f64 y4 b) (*.f64 y5 i)))) (*.f64 (-.f64 (*.f64 t y2) (*.f64 y y3)) (-.f64 (*.f64 y4 c) (*.f64 y5 a)))) (*.f64 (-.f64 (*.f64 k y2) (*.f64 j y3)) (-.f64 (*.f64 y4 y1) (*.f64 y5 y0))))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 42.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto y \cdot \left(\left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      2. mul-1-neg 42.0%

         \[\leadsto y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

   6. Simplified 42.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \leq \infty:\\ \;\;\;\;\left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \]

Alternative 3: 42.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y5 \cdot \left(i \cdot t_1 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot t_4\right)\right)\\ t_6 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{+96}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -1.85 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -3.8 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -1.4 \cdot 10^{-189}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t_4 - t_1 \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.6 \cdot 10^{-272}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-234}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-38}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          y2
          (+
           (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4))))))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (* y5 (+ (* i t_1) (- (* a (- (* t y2) (* y y3))) (* y0 t_4)))))
        (t_6
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y5 -2.4e+162)
     t_5
     (if (<= y5 -1.75e+105)
       (* c (* x (- (* y0 y2) (* y i))))
       (if (<= y5 -1.9e+96)
         (* z (* a (- (* y1 y3) (* t b))))
         (if (<= y5 -1.85e-134)
           t_3
           (if (<= y5 -3.8e-169)
             (* z (* i (- (* t c) (* k y1))))
             (if (<= y5 -1.4e-189)
               (* y4 (+ (- (* y1 t_4) (* t_1 b)) (* c (- (* y y3) (* t y2)))))
               (if (<= y5 1.6e-272)
                 t_6
                 (if (<= y5 2.7e-234)
                   (* (- (* b j) (* c y2)) (* t y4))
                   (if (<= y5 1.25e-38)
                     t_6
                     (if (<= y5 5.6e-12)
                       (* a (* b (- (* x y) (* z t))))
                       (if (<= y5 1.3e+54) t_3 t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.4e+162) {
		tmp = t_5;
	} else if (y5 <= -1.75e+105) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -1.9e+96) {
		tmp = z * (a * ((y1 * y3) - (t * b)));
	} else if (y5 <= -1.85e-134) {
		tmp = t_3;
	} else if (y5 <= -3.8e-169) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (y5 <= -1.4e-189) {
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.6e-272) {
		tmp = t_6;
	} else if (y5 <= 2.7e-234) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (y5 <= 1.25e-38) {
		tmp = t_6;
	} else if (y5 <= 5.6e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 1.3e+54) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (c * y0) - (a * y1)
    t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    t_4 = (k * y2) - (j * y3)
    t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)))
    t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    if (y5 <= (-2.4d+162)) then
        tmp = t_5
    else if (y5 <= (-1.75d+105)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y5 <= (-1.9d+96)) then
        tmp = z * (a * ((y1 * y3) - (t * b)))
    else if (y5 <= (-1.85d-134)) then
        tmp = t_3
    else if (y5 <= (-3.8d-169)) then
        tmp = z * (i * ((t * c) - (k * y1)))
    else if (y5 <= (-1.4d-189)) then
        tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * ((y * y3) - (t * y2))))
    else if (y5 <= 1.6d-272) then
        tmp = t_6
    else if (y5 <= 2.7d-234) then
        tmp = ((b * j) - (c * y2)) * (t * y4)
    else if (y5 <= 1.25d-38) then
        tmp = t_6
    else if (y5 <= 5.6d-12) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y5 <= 1.3d+54) then
        tmp = t_3
    else
        tmp = t_5
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -2.4e+162) {
		tmp = t_5;
	} else if (y5 <= -1.75e+105) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -1.9e+96) {
		tmp = z * (a * ((y1 * y3) - (t * b)));
	} else if (y5 <= -1.85e-134) {
		tmp = t_3;
	} else if (y5 <= -3.8e-169) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (y5 <= -1.4e-189) {
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * ((y * y3) - (t * y2))));
	} else if (y5 <= 1.6e-272) {
		tmp = t_6;
	} else if (y5 <= 2.7e-234) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (y5 <= 1.25e-38) {
		tmp = t_6;
	} else if (y5 <= 5.6e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 1.3e+54) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (c * y0) - (a * y1)
	t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	t_4 = (k * y2) - (j * y3)
	t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)))
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -2.4e+162:
		tmp = t_5
	elif y5 <= -1.75e+105:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y5 <= -1.9e+96:
		tmp = z * (a * ((y1 * y3) - (t * b)))
	elif y5 <= -1.85e-134:
		tmp = t_3
	elif y5 <= -3.8e-169:
		tmp = z * (i * ((t * c) - (k * y1)))
	elif y5 <= -1.4e-189:
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * ((y * y3) - (t * y2))))
	elif y5 <= 1.6e-272:
		tmp = t_6
	elif y5 <= 2.7e-234:
		tmp = ((b * j) - (c * y2)) * (t * y4)
	elif y5 <= 1.25e-38:
		tmp = t_6
	elif y5 <= 5.6e-12:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y5 <= 1.3e+54:
		tmp = t_3
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y5 * Float64(Float64(i * t_1) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y0 * t_4))))
	t_6 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -2.4e+162)
		tmp = t_5;
	elseif (y5 <= -1.75e+105)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y5 <= -1.9e+96)
		tmp = Float64(z * Float64(a * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (y5 <= -1.85e-134)
		tmp = t_3;
	elseif (y5 <= -3.8e-169)
		tmp = Float64(z * Float64(i * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (y5 <= -1.4e-189)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_4) - Float64(t_1 * b)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 1.6e-272)
		tmp = t_6;
	elseif (y5 <= 2.7e-234)
		tmp = Float64(Float64(Float64(b * j) - Float64(c * y2)) * Float64(t * y4));
	elseif (y5 <= 1.25e-38)
		tmp = t_6;
	elseif (y5 <= 5.6e-12)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y5 <= 1.3e+54)
		tmp = t_3;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (c * y0) - (a * y1);
	t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	t_4 = (k * y2) - (j * y3);
	t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -2.4e+162)
		tmp = t_5;
	elseif (y5 <= -1.75e+105)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y5 <= -1.9e+96)
		tmp = z * (a * ((y1 * y3) - (t * b)));
	elseif (y5 <= -1.85e-134)
		tmp = t_3;
	elseif (y5 <= -3.8e-169)
		tmp = z * (i * ((t * c) - (k * y1)));
	elseif (y5 <= -1.4e-189)
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * ((y * y3) - (t * y2))));
	elseif (y5 <= 1.6e-272)
		tmp = t_6;
	elseif (y5 <= 2.7e-234)
		tmp = ((b * j) - (c * y2)) * (t * y4);
	elseif (y5 <= 1.25e-38)
		tmp = t_6;
	elseif (y5 <= 5.6e-12)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y5 <= 1.3e+54)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(i * t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.4e+162], t$95$5, If[LessEqual[y5, -1.75e+105], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.9e+96], N[(z * N[(a * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.85e-134], t$95$3, If[LessEqual[y5, -3.8e-169], N[(z * N[(i * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.4e-189], N[(y4 * N[(N[(N[(y1 * t$95$4), $MachinePrecision] - N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.6e-272], t$95$6, If[LessEqual[y5, 2.7e-234], N[(N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision] * N[(t * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.25e-38], t$95$6, If[LessEqual[y5, 5.6e-12], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.3e+54], t$95$3, t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -2.40000000000000009e162 or 1.30000000000000003e54 < y5

   1. Initial program 17.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 64.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.2%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 64.2%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if -2.40000000000000009e162 < y5 < -1.74999999999999996e105

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 40.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 70.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -1.74999999999999996e105 < y5 < -1.9000000000000001e96

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 34.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in a around inf 67.4%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot z\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 67.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \cdot z\right) \]

      2. sub-neg 67.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \cdot z\right) \]

      3. *-commutative 67.4%

         \[\leadsto -1 \cdot \left(\left(a \cdot \left(t \cdot b - \color{blue}{y3 \cdot y1}\right)\right) \cdot z\right) \]

   7. Simplified 67.4%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot \left(t \cdot b - y3 \cdot y1\right)\right)} \cdot z\right) \]

   if -1.9000000000000001e96 < y5 < -1.85e-134 or 5.6000000000000004e-12 < y5 < 1.30000000000000003e54

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 54.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   if -1.85e-134 < y5 < -3.8e-169

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 46.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in i around inf 55.6%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot \left(i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot i\right) \cdot z\right)} \]

      2. distribute-lft-out-- 55.7%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(c \cdot t - k \cdot y1\right)\right)} \cdot i\right) \cdot z\right) \]

      3. associate-*r* 55.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-1 \cdot \left(\left(c \cdot t - k \cdot y1\right) \cdot i\right)\right)} \cdot z\right) \]

      4. mul-1-neg 55.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-\left(c \cdot t - k \cdot y1\right) \cdot i\right)} \cdot z\right) \]

      5. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(\left(-\color{blue}{i \cdot \left(c \cdot t - k \cdot y1\right)}\right) \cdot z\right) \]

      6. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(\left(-i \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \cdot z\right) \]

   7. Simplified 55.7%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-i \cdot \left(t \cdot c - k \cdot y1\right)\right) \cdot z\right)} \]

   if -3.8e-169 < y5 < -1.4e-189

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 100.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.4e-189 < y5 < 1.6e-272 or 2.7000000000000002e-234 < y5 < 1.25000000000000008e-38

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 53.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if 1.6e-272 < y5 < 2.7000000000000002e-234

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 83.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 83.9%

         \[\leadsto \color{blue}{\left(y4 \cdot t\right) \cdot \left(j \cdot b - c \cdot y2\right)} \]

      2. *-commutative 83.9%

         \[\leadsto \color{blue}{\left(t \cdot y4\right)} \cdot \left(j \cdot b - c \cdot y2\right) \]

      3. *-commutative 83.9%

         \[\leadsto \left(t \cdot y4\right) \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right) \]

   7. Simplified 83.9%

      \[\leadsto \color{blue}{\left(t \cdot y4\right) \cdot \left(j \cdot b - y2 \cdot c\right)} \]

   if 1.25000000000000008e-38 < y5 < 5.6000000000000004e-12

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 71.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 71.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 86.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.75 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{+96}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -1.85 \cdot 10^{-134}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -3.8 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -1.4 \cdot 10^{-189}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.6 \cdot 10^{-272}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-234}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 1.25 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \end{array} \]

Alternative 4: 39.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := c \cdot y4 - a \cdot y5\\ t_4 := y \cdot y3 - t \cdot y2\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := a \cdot b - c \cdot i\\ t_7 := y \cdot k - t \cdot j\\ t_8 := y5 \cdot t_1\\ t_9 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_6 + y2 \cdot t_2\right) + j \cdot t_5\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;a \cdot t_8\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot t_4\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_6\right) + y3 \cdot t_3\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot t_2 + \left(t_9 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t_1 \cdot t_3\right)\\ \mathbf{elif}\;j \leq 6.9 \cdot 10^{+40}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t_9 - t_7 \cdot b\right) + c \cdot t_4\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(t_8 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+212}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_7 + \left(a \cdot t_1 - y0 \cdot t_9\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+306}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t_5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* c y4) (* a y5)))
        (t_4 (- (* y y3) (* t y2)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (- (* a b) (* c i)))
        (t_7 (- (* y k) (* t j)))
        (t_8 (* y5 t_1))
        (t_9 (- (* k y2) (* j y3))))
   (if (<= j -2.4e+149)
     (* x (+ (+ (* y t_6) (* y2 t_2)) (* j t_5)))
     (if (<= j -2.1e+67)
       (* a t_8)
       (if (<= j -3.6e-263)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 t_4)))
         (if (<= j 8.5e-130)
           (* y (+ (+ (* k (- (* i y5) (* b y4))) (* x t_6)) (* y3 t_3)))
           (if (<= j 1.55e-51)
             (+
              (* (* x y2) t_2)
              (- (* t_9 (- (* y1 y4) (* y0 y5))) (* t_1 t_3)))
             (if (<= j 6.9e+40)
               (* y4 (+ (- (* y1 t_9) (* t_7 b)) (* c t_4)))
               (if (<= j 4.3e+142)
                 (*
                  a
                  (+
                   (* b (- (* x y) (* z t)))
                   (+ t_8 (* y1 (- (* z y3) (* x y2))))))
                 (if (<= j 2.1e+212)
                   (* y5 (+ (* i t_7) (- (* a t_1) (* y0 t_9))))
                   (if (<= j 1.45e+306)
                     (*
                      j
                      (+
                       (+
                        (* y3 (- (* y0 y5) (* y1 y4)))
                        (* t (- (* b y4) (* i y5))))
                       (* x t_5)))
                     (* (* t y5) (- (* a y2) (* i j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * b) - (c * i);
	double t_7 = (y * k) - (t * j);
	double t_8 = y5 * t_1;
	double t_9 = (k * y2) - (j * y3);
	double tmp;
	if (j <= -2.4e+149) {
		tmp = x * (((y * t_6) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -2.1e+67) {
		tmp = a * t_8;
	} else if (j <= -3.6e-263) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (j <= 8.5e-130) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	} else if (j <= 1.55e-51) {
		tmp = ((x * y2) * t_2) + ((t_9 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	} else if (j <= 6.9e+40) {
		tmp = y4 * (((y1 * t_9) - (t_7 * b)) + (c * t_4));
	} else if (j <= 4.3e+142) {
		tmp = a * ((b * ((x * y) - (z * t))) + (t_8 + (y1 * ((z * y3) - (x * y2)))));
	} else if (j <= 2.1e+212) {
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_9)));
	} else if (j <= 1.45e+306) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	} else {
		tmp = (t * y5) * ((a * y2) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (c * y0) - (a * y1)
    t_3 = (c * y4) - (a * y5)
    t_4 = (y * y3) - (t * y2)
    t_5 = (i * y1) - (b * y0)
    t_6 = (a * b) - (c * i)
    t_7 = (y * k) - (t * j)
    t_8 = y5 * t_1
    t_9 = (k * y2) - (j * y3)
    if (j <= (-2.4d+149)) then
        tmp = x * (((y * t_6) + (y2 * t_2)) + (j * t_5))
    else if (j <= (-2.1d+67)) then
        tmp = a * t_8
    else if (j <= (-3.6d-263)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
    else if (j <= 8.5d-130) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3))
    else if (j <= 1.55d-51) then
        tmp = ((x * y2) * t_2) + ((t_9 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3))
    else if (j <= 6.9d+40) then
        tmp = y4 * (((y1 * t_9) - (t_7 * b)) + (c * t_4))
    else if (j <= 4.3d+142) then
        tmp = a * ((b * ((x * y) - (z * t))) + (t_8 + (y1 * ((z * y3) - (x * y2)))))
    else if (j <= 2.1d+212) then
        tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_9)))
    else if (j <= 1.45d+306) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
    else
        tmp = (t * y5) * ((a * y2) - (i * j))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * b) - (c * i);
	double t_7 = (y * k) - (t * j);
	double t_8 = y5 * t_1;
	double t_9 = (k * y2) - (j * y3);
	double tmp;
	if (j <= -2.4e+149) {
		tmp = x * (((y * t_6) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -2.1e+67) {
		tmp = a * t_8;
	} else if (j <= -3.6e-263) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (j <= 8.5e-130) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	} else if (j <= 1.55e-51) {
		tmp = ((x * y2) * t_2) + ((t_9 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	} else if (j <= 6.9e+40) {
		tmp = y4 * (((y1 * t_9) - (t_7 * b)) + (c * t_4));
	} else if (j <= 4.3e+142) {
		tmp = a * ((b * ((x * y) - (z * t))) + (t_8 + (y1 * ((z * y3) - (x * y2)))));
	} else if (j <= 2.1e+212) {
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_9)));
	} else if (j <= 1.45e+306) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	} else {
		tmp = (t * y5) * ((a * y2) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (c * y0) - (a * y1)
	t_3 = (c * y4) - (a * y5)
	t_4 = (y * y3) - (t * y2)
	t_5 = (i * y1) - (b * y0)
	t_6 = (a * b) - (c * i)
	t_7 = (y * k) - (t * j)
	t_8 = y5 * t_1
	t_9 = (k * y2) - (j * y3)
	tmp = 0
	if j <= -2.4e+149:
		tmp = x * (((y * t_6) + (y2 * t_2)) + (j * t_5))
	elif j <= -2.1e+67:
		tmp = a * t_8
	elif j <= -3.6e-263:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
	elif j <= 8.5e-130:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3))
	elif j <= 1.55e-51:
		tmp = ((x * y2) * t_2) + ((t_9 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3))
	elif j <= 6.9e+40:
		tmp = y4 * (((y1 * t_9) - (t_7 * b)) + (c * t_4))
	elif j <= 4.3e+142:
		tmp = a * ((b * ((x * y) - (z * t))) + (t_8 + (y1 * ((z * y3) - (x * y2)))))
	elif j <= 2.1e+212:
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_9)))
	elif j <= 1.45e+306:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
	else:
		tmp = (t * y5) * ((a * y2) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	t_4 = Float64(Float64(y * y3) - Float64(t * y2))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(Float64(a * b) - Float64(c * i))
	t_7 = Float64(Float64(y * k) - Float64(t * j))
	t_8 = Float64(y5 * t_1)
	t_9 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (j <= -2.4e+149)
		tmp = Float64(x * Float64(Float64(Float64(y * t_6) + Float64(y2 * t_2)) + Float64(j * t_5)));
	elseif (j <= -2.1e+67)
		tmp = Float64(a * t_8);
	elseif (j <= -3.6e-263)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * t_4)));
	elseif (j <= 8.5e-130)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_6)) + Float64(y3 * t_3)));
	elseif (j <= 1.55e-51)
		tmp = Float64(Float64(Float64(x * y2) * t_2) + Float64(Float64(t_9 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(t_1 * t_3)));
	elseif (j <= 6.9e+40)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_9) - Float64(t_7 * b)) + Float64(c * t_4)));
	elseif (j <= 4.3e+142)
		tmp = Float64(a * Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(t_8 + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (j <= 2.1e+212)
		tmp = Float64(y5 * Float64(Float64(i * t_7) + Float64(Float64(a * t_1) - Float64(y0 * t_9))));
	elseif (j <= 1.45e+306)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_5)));
	else
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	t_2 = (c * y0) - (a * y1);
	t_3 = (c * y4) - (a * y5);
	t_4 = (y * y3) - (t * y2);
	t_5 = (i * y1) - (b * y0);
	t_6 = (a * b) - (c * i);
	t_7 = (y * k) - (t * j);
	t_8 = y5 * t_1;
	t_9 = (k * y2) - (j * y3);
	tmp = 0.0;
	if (j <= -2.4e+149)
		tmp = x * (((y * t_6) + (y2 * t_2)) + (j * t_5));
	elseif (j <= -2.1e+67)
		tmp = a * t_8;
	elseif (j <= -3.6e-263)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	elseif (j <= 8.5e-130)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	elseif (j <= 1.55e-51)
		tmp = ((x * y2) * t_2) + ((t_9 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	elseif (j <= 6.9e+40)
		tmp = y4 * (((y1 * t_9) - (t_7 * b)) + (c * t_4));
	elseif (j <= 4.3e+142)
		tmp = a * ((b * ((x * y) - (z * t))) + (t_8 + (y1 * ((z * y3) - (x * y2)))));
	elseif (j <= 2.1e+212)
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_9)));
	elseif (j <= 1.45e+306)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	else
		tmp = (t * y5) * ((a * y2) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(y5 * t$95$1), $MachinePrecision]}, Block[{t$95$9 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e+149], N[(x * N[(N[(N[(y * t$95$6), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e+67], N[(a * t$95$8), $MachinePrecision], If[LessEqual[j, -3.6e-263], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-130], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e-51], N[(N[(N[(x * y2), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(t$95$9 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.9e+40], N[(y4 * N[(N[(N[(y1 * t$95$9), $MachinePrecision] - N[(t$95$7 * b), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.3e+142], N[(a * N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e+212], N[(y5 * N[(N[(i * t$95$7), $MachinePrecision] + N[(N[(a * t$95$1), $MachinePrecision] - N[(y0 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+306], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if j < -2.40000000000000012e149

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 50.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -2.40000000000000012e149 < j < -2.1000000000000001e67

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 67.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -2.1000000000000001e67 < j < -3.6e-263

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 60.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.6e-263 < j < 8.50000000000000033e-130

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.7%

         \[\leadsto y \cdot \left(\left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      2. mul-1-neg 59.7%

         \[\leadsto y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 8.50000000000000033e-130 < j < 1.5499999999999999e-51

   1. Initial program 57.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 57.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 57.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 79.0%

      \[\leadsto \color{blue}{\left(c \cdot y0 - y1 \cdot a\right) \cdot \left(y2 \cdot x\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   if 1.5499999999999999e-51 < j < 6.9000000000000003e40

   1. Initial program 6.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 6.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 6.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 62.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 6.9000000000000003e40 < j < 4.30000000000000012e142

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 13.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 13.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 54.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 54.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 54.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 54.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   if 4.30000000000000012e142 < j < 2.1e212

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 68.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 68.7%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if 2.1e212 < j < 1.45000000000000005e306

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 18.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 63.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   if 1.45000000000000005e306 < j

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around inf 100.0%

      \[\leadsto -\color{blue}{\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]
   8. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto -\left(\color{blue}{j \cdot i} - a \cdot y2\right) \cdot \left(t \cdot y5\right) \]

      2. *-commutative 100.0%

         \[\leadsto -\left(j \cdot i - \color{blue}{y2 \cdot a}\right) \cdot \left(t \cdot y5\right) \]

      3. *-commutative 100.0%

         \[\leadsto -\left(j \cdot i - y2 \cdot a\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   9. Simplified 100.0%

      \[\leadsto -\color{blue}{\left(j \cdot i - y2 \cdot a\right) \cdot \left(y5 \cdot t\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 6.9 \cdot 10^{+40}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+212}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+306}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \end{array} \]

Alternative 5: 38.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := c \cdot y4 - a \cdot y5\\ t_4 := y \cdot y3 - t \cdot y2\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := a \cdot b - c \cdot i\\ t_7 := y \cdot k - t \cdot j\\ \mathbf{if}\;j \leq -4.8 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_6 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_5\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y5 \cdot t_1\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot t_4\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_6\right) + y3 \cdot t_3\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot t_7 + \left(t_2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t_1 \cdot t_3\right)\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t_2 - t_7 \cdot b\right) + c \cdot t_4\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+219}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_7 + \left(a \cdot t_1 - y0 \cdot t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (- (* c y4) (* a y5)))
        (t_4 (- (* y y3) (* t y2)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (- (* a b) (* c i)))
        (t_7 (- (* y k) (* t j))))
   (if (<= j -4.8e+149)
     (* x (+ (+ (* y t_6) (* y2 (- (* c y0) (* a y1)))) (* j t_5)))
     (if (<= j -1.15e+67)
       (* a (* y5 t_1))
       (if (<= j -3.6e-263)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 t_4)))
         (if (<= j 2e-267)
           (* y (+ (+ (* k (- (* i y5) (* b y4))) (* x t_6)) (* y3 t_3)))
           (if (<= j 2.05e-52)
             (+
              (* (* i y5) t_7)
              (- (* t_2 (- (* y1 y4) (* y0 y5))) (* t_1 t_3)))
             (if (<= j 7.1e+19)
               (* y4 (+ (- (* y1 t_2) (* t_7 b)) (* c t_4)))
               (if (<= j 1.65e+152)
                 (* a (* y2 (- (* t y5) (* x y1))))
                 (if (<= j 1.35e+219)
                   (* y5 (+ (* i t_7) (- (* a t_1) (* y0 t_2))))
                   (*
                    j
                    (+
                     (+
                      (* y3 (- (* y0 y5) (* y1 y4)))
                      (* t (- (* b y4) (* i y5))))
                     (* x t_5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * b) - (c * i);
	double t_7 = (y * k) - (t * j);
	double tmp;
	if (j <= -4.8e+149) {
		tmp = x * (((y * t_6) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else if (j <= -1.15e+67) {
		tmp = a * (y5 * t_1);
	} else if (j <= -3.6e-263) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (j <= 2e-267) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	} else if (j <= 2.05e-52) {
		tmp = ((i * y5) * t_7) + ((t_2 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	} else if (j <= 7.1e+19) {
		tmp = y4 * (((y1 * t_2) - (t_7 * b)) + (c * t_4));
	} else if (j <= 1.65e+152) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (j <= 1.35e+219) {
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_2)));
	} else {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (k * y2) - (j * y3)
    t_3 = (c * y4) - (a * y5)
    t_4 = (y * y3) - (t * y2)
    t_5 = (i * y1) - (b * y0)
    t_6 = (a * b) - (c * i)
    t_7 = (y * k) - (t * j)
    if (j <= (-4.8d+149)) then
        tmp = x * (((y * t_6) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
    else if (j <= (-1.15d+67)) then
        tmp = a * (y5 * t_1)
    else if (j <= (-3.6d-263)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
    else if (j <= 2d-267) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3))
    else if (j <= 2.05d-52) then
        tmp = ((i * y5) * t_7) + ((t_2 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3))
    else if (j <= 7.1d+19) then
        tmp = y4 * (((y1 * t_2) - (t_7 * b)) + (c * t_4))
    else if (j <= 1.65d+152) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (j <= 1.35d+219) then
        tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_2)))
    else
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (c * y4) - (a * y5);
	double t_4 = (y * y3) - (t * y2);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (a * b) - (c * i);
	double t_7 = (y * k) - (t * j);
	double tmp;
	if (j <= -4.8e+149) {
		tmp = x * (((y * t_6) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else if (j <= -1.15e+67) {
		tmp = a * (y5 * t_1);
	} else if (j <= -3.6e-263) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	} else if (j <= 2e-267) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	} else if (j <= 2.05e-52) {
		tmp = ((i * y5) * t_7) + ((t_2 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	} else if (j <= 7.1e+19) {
		tmp = y4 * (((y1 * t_2) - (t_7 * b)) + (c * t_4));
	} else if (j <= 1.65e+152) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (j <= 1.35e+219) {
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_2)));
	} else {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (k * y2) - (j * y3)
	t_3 = (c * y4) - (a * y5)
	t_4 = (y * y3) - (t * y2)
	t_5 = (i * y1) - (b * y0)
	t_6 = (a * b) - (c * i)
	t_7 = (y * k) - (t * j)
	tmp = 0
	if j <= -4.8e+149:
		tmp = x * (((y * t_6) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
	elif j <= -1.15e+67:
		tmp = a * (y5 * t_1)
	elif j <= -3.6e-263:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4))
	elif j <= 2e-267:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3))
	elif j <= 2.05e-52:
		tmp = ((i * y5) * t_7) + ((t_2 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3))
	elif j <= 7.1e+19:
		tmp = y4 * (((y1 * t_2) - (t_7 * b)) + (c * t_4))
	elif j <= 1.65e+152:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif j <= 1.35e+219:
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_2)))
	else:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(Float64(c * y4) - Float64(a * y5))
	t_4 = Float64(Float64(y * y3) - Float64(t * y2))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(Float64(a * b) - Float64(c * i))
	t_7 = Float64(Float64(y * k) - Float64(t * j))
	tmp = 0.0
	if (j <= -4.8e+149)
		tmp = Float64(x * Float64(Float64(Float64(y * t_6) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_5)));
	elseif (j <= -1.15e+67)
		tmp = Float64(a * Float64(y5 * t_1));
	elseif (j <= -3.6e-263)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * t_4)));
	elseif (j <= 2e-267)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_6)) + Float64(y3 * t_3)));
	elseif (j <= 2.05e-52)
		tmp = Float64(Float64(Float64(i * y5) * t_7) + Float64(Float64(t_2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(t_1 * t_3)));
	elseif (j <= 7.1e+19)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_2) - Float64(t_7 * b)) + Float64(c * t_4)));
	elseif (j <= 1.65e+152)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (j <= 1.35e+219)
		tmp = Float64(y5 * Float64(Float64(i * t_7) + Float64(Float64(a * t_1) - Float64(y0 * t_2))));
	else
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	t_2 = (k * y2) - (j * y3);
	t_3 = (c * y4) - (a * y5);
	t_4 = (y * y3) - (t * y2);
	t_5 = (i * y1) - (b * y0);
	t_6 = (a * b) - (c * i);
	t_7 = (y * k) - (t * j);
	tmp = 0.0;
	if (j <= -4.8e+149)
		tmp = x * (((y * t_6) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	elseif (j <= -1.15e+67)
		tmp = a * (y5 * t_1);
	elseif (j <= -3.6e-263)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_4));
	elseif (j <= 2e-267)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_6)) + (y3 * t_3));
	elseif (j <= 2.05e-52)
		tmp = ((i * y5) * t_7) + ((t_2 * ((y1 * y4) - (y0 * y5))) - (t_1 * t_3));
	elseif (j <= 7.1e+19)
		tmp = y4 * (((y1 * t_2) - (t_7 * b)) + (c * t_4));
	elseif (j <= 1.65e+152)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (j <= 1.35e+219)
		tmp = y5 * ((i * t_7) + ((a * t_1) - (y0 * t_2)));
	else
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.8e+149], N[(x * N[(N[(N[(y * t$95$6), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.15e+67], N[(a * N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-263], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-267], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e-52], N[(N[(N[(i * y5), $MachinePrecision] * t$95$7), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.1e+19], N[(y4 * N[(N[(N[(y1 * t$95$2), $MachinePrecision] - N[(t$95$7 * b), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e+152], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e+219], N[(y5 * N[(N[(i * t$95$7), $MachinePrecision] + N[(N[(a * t$95$1), $MachinePrecision] - N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -4.80000000000000024e149

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 50.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -4.80000000000000024e149 < j < -1.1499999999999999e67

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 67.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -1.1499999999999999e67 < j < -3.6e-263

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 60.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.6e-263 < j < 2e-267

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 40.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto y \cdot \left(\left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      2. mul-1-neg 80.4%

         \[\leadsto y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

   6. Simplified 80.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 2e-267 < j < 2.04999999999999994e-52

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around inf 56.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot \left(i \cdot y5\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto \color{blue}{\left(-\left(t \cdot j - k \cdot y\right) \cdot \left(i \cdot y5\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{\left(-\left(t \cdot j - k \cdot y\right) \cdot \left(i \cdot y5\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   if 2.04999999999999994e-52 < j < 7.1e19

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 72.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 7.1e19 < j < 1.6500000000000001e152

   1. Initial program 10.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 10.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 10.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 41.5%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 41.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 41.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 41.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 41.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 51.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if 1.6500000000000001e152 < j < 1.3499999999999999e219

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 65.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.2%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 65.2%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 65.2%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if 1.3499999999999999e219 < j

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 18.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 22.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 59.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-52}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.1 \cdot 10^{+19}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+219}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 6: 36.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot t_1\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-10}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq -1.25 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq -6 \cdot 10^{-192}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-223}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq 2.25 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{-85}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          y2
          (+
           (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4))))))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y4 -1.45e+110)
     (*
      y4
      (+ (- (* y1 (- (* k y2) (* j y3))) (* (- (* y k) (* t j)) b)) (* c t_1)))
     (if (<= y4 -8e-10)
       t_4
       (if (<= y4 -1.25e-111)
         t_3
         (if (<= y4 -1e-165)
           (* a (* y2 (- (* t y5) (* x y1))))
           (if (<= y4 -6e-192)
             (* k (- (* i (* z y1))))
             (if (<= y4 -5.6e-223)
               t_4
               (if (<= y4 2.25e-262)
                 t_3
                 (if (<= y4 4.4e-132)
                   (* c (* x (- (* y0 y2) (* y i))))
                   (if (<= y4 2e-85)
                     (* (* t y5) (- (* a y2) (* i j)))
                     (if (<= y4 1.4e-38) t_4 (* (* c y4) t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -1.45e+110) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * t_1));
	} else if (y4 <= -8e-10) {
		tmp = t_4;
	} else if (y4 <= -1.25e-111) {
		tmp = t_3;
	} else if (y4 <= -1e-165) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y4 <= -6e-192) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= -5.6e-223) {
		tmp = t_4;
	} else if (y4 <= 2.25e-262) {
		tmp = t_3;
	} else if (y4 <= 4.4e-132) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y4 <= 2e-85) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y4 <= 1.4e-38) {
		tmp = t_4;
	} else {
		tmp = (c * y4) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = (c * y0) - (a * y1)
    t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    if (y4 <= (-1.45d+110)) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * t_1))
    else if (y4 <= (-8d-10)) then
        tmp = t_4
    else if (y4 <= (-1.25d-111)) then
        tmp = t_3
    else if (y4 <= (-1d-165)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y4 <= (-6d-192)) then
        tmp = k * -(i * (z * y1))
    else if (y4 <= (-5.6d-223)) then
        tmp = t_4
    else if (y4 <= 2.25d-262) then
        tmp = t_3
    else if (y4 <= 4.4d-132) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y4 <= 2d-85) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y4 <= 1.4d-38) then
        tmp = t_4
    else
        tmp = (c * y4) * t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -1.45e+110) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * t_1));
	} else if (y4 <= -8e-10) {
		tmp = t_4;
	} else if (y4 <= -1.25e-111) {
		tmp = t_3;
	} else if (y4 <= -1e-165) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y4 <= -6e-192) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= -5.6e-223) {
		tmp = t_4;
	} else if (y4 <= 2.25e-262) {
		tmp = t_3;
	} else if (y4 <= 4.4e-132) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y4 <= 2e-85) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y4 <= 1.4e-38) {
		tmp = t_4;
	} else {
		tmp = (c * y4) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = (c * y0) - (a * y1)
	t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y4 <= -1.45e+110:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * t_1))
	elif y4 <= -8e-10:
		tmp = t_4
	elif y4 <= -1.25e-111:
		tmp = t_3
	elif y4 <= -1e-165:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y4 <= -6e-192:
		tmp = k * -(i * (z * y1))
	elif y4 <= -5.6e-223:
		tmp = t_4
	elif y4 <= 2.25e-262:
		tmp = t_3
	elif y4 <= 4.4e-132:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y4 <= 2e-85:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y4 <= 1.4e-38:
		tmp = t_4
	else:
		tmp = (c * y4) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y4 <= -1.45e+110)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(Float64(Float64(y * k) - Float64(t * j)) * b)) + Float64(c * t_1)));
	elseif (y4 <= -8e-10)
		tmp = t_4;
	elseif (y4 <= -1.25e-111)
		tmp = t_3;
	elseif (y4 <= -1e-165)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y4 <= -6e-192)
		tmp = Float64(k * Float64(-Float64(i * Float64(z * y1))));
	elseif (y4 <= -5.6e-223)
		tmp = t_4;
	elseif (y4 <= 2.25e-262)
		tmp = t_3;
	elseif (y4 <= 4.4e-132)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y4 <= 2e-85)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y4 <= 1.4e-38)
		tmp = t_4;
	else
		tmp = Float64(Float64(c * y4) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * y3) - (t * y2);
	t_2 = (c * y0) - (a * y1);
	t_3 = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y4 <= -1.45e+110)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * t_1));
	elseif (y4 <= -8e-10)
		tmp = t_4;
	elseif (y4 <= -1.25e-111)
		tmp = t_3;
	elseif (y4 <= -1e-165)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y4 <= -6e-192)
		tmp = k * -(i * (z * y1));
	elseif (y4 <= -5.6e-223)
		tmp = t_4;
	elseif (y4 <= 2.25e-262)
		tmp = t_3;
	elseif (y4 <= 4.4e-132)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y4 <= 2e-85)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y4 <= 1.4e-38)
		tmp = t_4;
	else
		tmp = (c * y4) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.45e+110], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8e-10], t$95$4, If[LessEqual[y4, -1.25e-111], t$95$3, If[LessEqual[y4, -1e-165], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6e-192], N[(k * (-N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y4, -5.6e-223], t$95$4, If[LessEqual[y4, 2.25e-262], t$95$3, If[LessEqual[y4, 4.4e-132], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2e-85], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.4e-38], t$95$4, N[(N[(c * y4), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -1.45e110

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 67.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.45e110 < y4 < -8.00000000000000029e-10 or -5.9999999999999998e-192 < y4 < -5.6000000000000003e-223 or 2e-85 < y4 < 1.4e-38

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 60.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -8.00000000000000029e-10 < y4 < -1.2500000000000001e-111 or -5.6000000000000003e-223 < y4 < 2.24999999999999999e-262

   1. Initial program 15.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 56.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   if -1.2500000000000001e-111 < y4 < -1e-165

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 53.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 53.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 53.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 53.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 53.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 48.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if -1e-165 < y4 < -5.9999999999999998e-192

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 39.3%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 27.4%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot z\right) \cdot y1\right)}\right) \]

      2. associate-*r* 63.2%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(z \cdot y1\right)\right)}\right) \]

   8. Simplified 63.2%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right)\right)} \]

   if 2.24999999999999999e-262 < y4 < 4.39999999999999981e-132

   1. Initial program 47.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 47.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 65.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 65.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if 4.39999999999999981e-132 < y4 < 2e-85

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 78.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.1%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 78.1%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 78.1%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around inf 68.3%

      \[\leadsto -\color{blue}{\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]
   8. Step-by-step derivation

      1. *-commutative 68.3%

         \[\leadsto -\left(\color{blue}{j \cdot i} - a \cdot y2\right) \cdot \left(t \cdot y5\right) \]

      2. *-commutative 68.3%

         \[\leadsto -\left(j \cdot i - \color{blue}{y2 \cdot a}\right) \cdot \left(t \cdot y5\right) \]

      3. *-commutative 68.3%

         \[\leadsto -\left(j \cdot i - y2 \cdot a\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   9. Simplified 68.3%

      \[\leadsto -\color{blue}{\left(j \cdot i - y2 \cdot a\right) \cdot \left(y5 \cdot t\right)} \]

   if 1.4e-38 < y4

   1. Initial program 13.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 13.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 13.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 54.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.25 \cdot 10^{-111}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq -6 \cdot 10^{-192}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 2.25 \cdot 10^{-262}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{-85}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \end{array} \]

Alternative 7: 34.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+157}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+33}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 0.0064:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 10^{+113}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* (- (* y k) (* t j)) b))
           (* c (- (* y y3) (* t y2))))))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= a -3.6e+157)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= a -1.5e+63)
       t_1
       (if (<= a -6e+33)
         (* (* y2 y4) (- (* k y1) (* t c)))
         (if (<= a -7.5e+19)
           (* c (* y (- (* y3 y4) (* x i))))
           (if (<= a -7e-227)
             t_2
             (if (<= a -5e-303)
               t_1
               (if (<= a 9.5e-172)
                 (* c (* x (- (* y0 y2) (* y i))))
                 (if (<= a 0.0064)
                   (* z (* i (- (* t c) (* k y1))))
                   (if (<= a 8.8e+55)
                     t_2
                     (if (<= a 2.7e+86)
                       (* z (* k (- (* b y0) (* i y1))))
                       (if (<= a 1e+113)
                         (* (* t a) (- (* y2 y5) (* z b)))
                         (* (* y a) (- (* x b) (* y3 y5))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (a <= -3.6e+157) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -1.5e+63) {
		tmp = t_1;
	} else if (a <= -6e+33) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (a <= -7.5e+19) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= -7e-227) {
		tmp = t_2;
	} else if (a <= -5e-303) {
		tmp = t_1;
	} else if (a <= 9.5e-172) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 0.0064) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (a <= 8.8e+55) {
		tmp = t_2;
	} else if (a <= 2.7e+86) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else if (a <= 1e+113) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))))
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (a <= (-3.6d+157)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (a <= (-1.5d+63)) then
        tmp = t_1
    else if (a <= (-6d+33)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (a <= (-7.5d+19)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= (-7d-227)) then
        tmp = t_2
    else if (a <= (-5d-303)) then
        tmp = t_1
    else if (a <= 9.5d-172) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (a <= 0.0064d0) then
        tmp = z * (i * ((t * c) - (k * y1)))
    else if (a <= 8.8d+55) then
        tmp = t_2
    else if (a <= 2.7d+86) then
        tmp = z * (k * ((b * y0) - (i * y1)))
    else if (a <= 1d+113) then
        tmp = (t * a) * ((y2 * y5) - (z * b))
    else
        tmp = (y * a) * ((x * b) - (y3 * y5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (a <= -3.6e+157) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -1.5e+63) {
		tmp = t_1;
	} else if (a <= -6e+33) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (a <= -7.5e+19) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= -7e-227) {
		tmp = t_2;
	} else if (a <= -5e-303) {
		tmp = t_1;
	} else if (a <= 9.5e-172) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 0.0064) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (a <= 8.8e+55) {
		tmp = t_2;
	} else if (a <= 2.7e+86) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else if (a <= 1e+113) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))))
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if a <= -3.6e+157:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif a <= -1.5e+63:
		tmp = t_1
	elif a <= -6e+33:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif a <= -7.5e+19:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= -7e-227:
		tmp = t_2
	elif a <= -5e-303:
		tmp = t_1
	elif a <= 9.5e-172:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif a <= 0.0064:
		tmp = z * (i * ((t * c) - (k * y1)))
	elif a <= 8.8e+55:
		tmp = t_2
	elif a <= 2.7e+86:
		tmp = z * (k * ((b * y0) - (i * y1)))
	elif a <= 1e+113:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	else:
		tmp = (y * a) * ((x * b) - (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(Float64(Float64(y * k) - Float64(t * j)) * b)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (a <= -3.6e+157)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (a <= -1.5e+63)
		tmp = t_1;
	elseif (a <= -6e+33)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (a <= -7.5e+19)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= -7e-227)
		tmp = t_2;
	elseif (a <= -5e-303)
		tmp = t_1;
	elseif (a <= 9.5e-172)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (a <= 0.0064)
		tmp = Float64(z * Float64(i * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (a <= 8.8e+55)
		tmp = t_2;
	elseif (a <= 2.7e+86)
		tmp = Float64(z * Float64(k * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (a <= 1e+113)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	else
		tmp = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (a <= -3.6e+157)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (a <= -1.5e+63)
		tmp = t_1;
	elseif (a <= -6e+33)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (a <= -7.5e+19)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= -7e-227)
		tmp = t_2;
	elseif (a <= -5e-303)
		tmp = t_1;
	elseif (a <= 9.5e-172)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (a <= 0.0064)
		tmp = z * (i * ((t * c) - (k * y1)));
	elseif (a <= 8.8e+55)
		tmp = t_2;
	elseif (a <= 2.7e+86)
		tmp = z * (k * ((b * y0) - (i * y1)));
	elseif (a <= 1e+113)
		tmp = (t * a) * ((y2 * y5) - (z * b));
	else
		tmp = (y * a) * ((x * b) - (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+157], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e+63], t$95$1, If[LessEqual[a, -6e+33], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e+19], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-227], t$95$2, If[LessEqual[a, -5e-303], t$95$1, If[LessEqual[a, 9.5e-172], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0064], N[(z * N[(i * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+55], t$95$2, If[LessEqual[a, 2.7e+86], N[(z * N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+113], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if a < -3.60000000000000024e157

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y5 around inf 66.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot \left(y5 \cdot y2\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 69.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y5\right) \cdot y2} \]

      2. *-commutative 69.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right)\right)} \cdot y2 \]

      3. associate-*l* 66.0%

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y2\right)} \]

      4. cancel-sign-sub-inv 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + \left(--1\right) \cdot \left(a \cdot t\right)\right)} \cdot y2\right) \]

      5. metadata-eval 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{1} \cdot \left(a \cdot t\right)\right) \cdot y2\right) \]

      6. *-lft-identity 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{a \cdot t}\right) \cdot y2\right) \]

      7. +-commutative 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t + -1 \cdot \left(k \cdot y0\right)\right)} \cdot y2\right) \]

      8. mul-1-neg 66.0%

         \[\leadsto y5 \cdot \left(\left(a \cdot t + \color{blue}{\left(-k \cdot y0\right)}\right) \cdot y2\right) \]

      9. unsub-neg 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t - k \cdot y0\right)} \cdot y2\right) \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{y5 \cdot \left(\left(a \cdot t - k \cdot y0\right) \cdot y2\right)} \]

   if -3.60000000000000024e157 < a < -1.5e63 or -7.0000000000000002e-227 < a < -4.9999999999999998e-303

   1. Initial program 17.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.5e63 < a < -5.99999999999999967e33

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 68.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.0%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 68.0%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 68.0%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   if -5.99999999999999967e33 < a < -7.5e19

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 80.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 80.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 80.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y around -inf 100.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 100.0%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 100.0%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 100.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if -7.5e19 < a < -7.0000000000000002e-227 or 0.00640000000000000031 < a < 8.80000000000000042e55

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 49.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -4.9999999999999998e-303 < a < 9.50000000000000053e-172

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if 9.50000000000000053e-172 < a < 0.00640000000000000031

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in i around inf 45.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot \left(i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot i\right) \cdot z\right)} \]

      2. distribute-lft-out-- 51.0%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(c \cdot t - k \cdot y1\right)\right)} \cdot i\right) \cdot z\right) \]

      3. associate-*r* 51.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-1 \cdot \left(\left(c \cdot t - k \cdot y1\right) \cdot i\right)\right)} \cdot z\right) \]

      4. mul-1-neg 51.0%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-\left(c \cdot t - k \cdot y1\right) \cdot i\right)} \cdot z\right) \]

      5. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(\left(-\color{blue}{i \cdot \left(c \cdot t - k \cdot y1\right)}\right) \cdot z\right) \]

      6. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(\left(-i \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \cdot z\right) \]

   7. Simplified 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-i \cdot \left(t \cdot c - k \cdot y1\right)\right) \cdot z\right)} \]

   if 8.80000000000000042e55 < a < 2.70000000000000018e86

   1. Initial program 9.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 73.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 73.6%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   if 2.70000000000000018e86 < a < 1e113

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 50.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 66.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 66.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 66.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 66.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 66.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in t around inf 84.1%

      \[\leadsto \color{blue}{\left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right) \cdot \left(a \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right)} \]

      2. *-commutative 84.1%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot \left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right) \]

      3. mul-1-neg 84.1%

         \[\leadsto \left(t \cdot a\right) \cdot \left(y5 \cdot y2 + \color{blue}{\left(-z \cdot b\right)}\right) \]

      4. unsub-neg 84.1%

         \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{\left(y5 \cdot y2 - z \cdot b\right)} \]

      5. *-commutative 84.1%

         \[\leadsto \left(t \cdot a\right) \cdot \left(y5 \cdot y2 - \color{blue}{b \cdot z}\right) \]

   9. Simplified 84.1%

      \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot \left(y5 \cdot y2 - b \cdot z\right)} \]

   if 1e113 < a

   1. Initial program 6.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 6.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 6.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 51.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 51.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 51.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 51.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.9%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 58.9%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. +-commutative 58.9%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      4. mul-1-neg 58.9%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      5. unsub-neg 58.9%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      6. *-commutative 58.9%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x - \color{blue}{y5 \cdot y3}\right) \]

   9. Simplified 58.9%

      \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x - y5 \cdot y3\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+157}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+63}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+33}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-303}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 0.0064:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 10^{+113}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \]

Alternative 8: 43.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -2.25 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -1.4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -1.28 \cdot 10^{-163}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (- (* a (- (* t y2) (* y y3))) (* y0 (- (* k y2) (* j y3)))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))))
   (if (<= y5 -1.8e+162)
     t_1
     (if (<= y5 -2.25e+114)
       (* c (* x (- (* y0 y2) (* y i))))
       (if (<= y5 -1.4e+32)
         t_1
         (if (<= y5 -3.2e-45)
           t_3
           (if (<= y5 -1.28e-163)
             (*
              z
              (+
               (* k (- (* b y0) (* i y1)))
               (+ (* y3 (- (* a y1) (* c y0))) (* t (- (* c i) (* a b))))))
             (if (<= y5 3.2e-234)
               t_3
               (if (<= y5 1.15e-38)
                 (*
                  x
                  (+
                   (+ (* y (- (* a b) (* c i))) (* y2 t_2))
                   (* j (- (* i y1) (* b y0)))))
                 (if (<= y5 3.1e-12)
                   (* a (* b (- (* x y) (* z t))))
                   (if (<= y5 2.4e+56)
                     (*
                      y2
                      (+
                       (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
                       (* t (- (* a y5) (* c y4)))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (y5 <= -1.8e+162) {
		tmp = t_1;
	} else if (y5 <= -2.25e+114) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -1.4e+32) {
		tmp = t_1;
	} else if (y5 <= -3.2e-45) {
		tmp = t_3;
	} else if (y5 <= -1.28e-163) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else if (y5 <= 3.2e-234) {
		tmp = t_3;
	} else if (y5 <= 1.15e-38) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 3.1e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 2.4e+56) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))))
    t_2 = (c * y0) - (a * y1)
    t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    if (y5 <= (-1.8d+162)) then
        tmp = t_1
    else if (y5 <= (-2.25d+114)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y5 <= (-1.4d+32)) then
        tmp = t_1
    else if (y5 <= (-3.2d-45)) then
        tmp = t_3
    else if (y5 <= (-1.28d-163)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
    else if (y5 <= 3.2d-234) then
        tmp = t_3
    else if (y5 <= 1.15d-38) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    else if (y5 <= 3.1d-12) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y5 <= 2.4d+56) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (y5 <= -1.8e+162) {
		tmp = t_1;
	} else if (y5 <= -2.25e+114) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -1.4e+32) {
		tmp = t_1;
	} else if (y5 <= -3.2e-45) {
		tmp = t_3;
	} else if (y5 <= -1.28e-163) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else if (y5 <= 3.2e-234) {
		tmp = t_3;
	} else if (y5 <= 1.15e-38) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 3.1e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 2.4e+56) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))))
	t_2 = (c * y0) - (a * y1)
	t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	tmp = 0
	if y5 <= -1.8e+162:
		tmp = t_1
	elif y5 <= -2.25e+114:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y5 <= -1.4e+32:
		tmp = t_1
	elif y5 <= -3.2e-45:
		tmp = t_3
	elif y5 <= -1.28e-163:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
	elif y5 <= 3.2e-234:
		tmp = t_3
	elif y5 <= 1.15e-38:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	elif y5 <= 3.1e-12:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y5 <= 2.4e+56:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3))))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y5 <= -1.8e+162)
		tmp = t_1;
	elseif (y5 <= -2.25e+114)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y5 <= -1.4e+32)
		tmp = t_1;
	elseif (y5 <= -3.2e-45)
		tmp = t_3;
	elseif (y5 <= -1.28e-163)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	elseif (y5 <= 3.2e-234)
		tmp = t_3;
	elseif (y5 <= 1.15e-38)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y5 <= 3.1e-12)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y5 <= 2.4e+56)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	t_2 = (c * y0) - (a * y1);
	t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y5 <= -1.8e+162)
		tmp = t_1;
	elseif (y5 <= -2.25e+114)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y5 <= -1.4e+32)
		tmp = t_1;
	elseif (y5 <= -3.2e-45)
		tmp = t_3;
	elseif (y5 <= -1.28e-163)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	elseif (y5 <= 3.2e-234)
		tmp = t_3;
	elseif (y5 <= 1.15e-38)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	elseif (y5 <= 3.1e-12)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y5 <= 2.4e+56)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.8e+162], t$95$1, If[LessEqual[y5, -2.25e+114], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.4e+32], t$95$1, If[LessEqual[y5, -3.2e-45], t$95$3, If[LessEqual[y5, -1.28e-163], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.2e-234], t$95$3, If[LessEqual[y5, 1.15e-38], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.1e-12], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e+56], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -1.79999999999999997e162 or -2.25e114 < y5 < -1.4e32 or 2.40000000000000013e56 < y5

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 63.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 63.2%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 63.2%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if -1.79999999999999997e162 < y5 < -2.25e114

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -1.4e32 < y5 < -3.20000000000000007e-45 or -1.28e-163 < y5 < 3.1999999999999999e-234

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 57.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 57.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.20000000000000007e-45 < y5 < -1.28e-163

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 52.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   if 3.1999999999999999e-234 < y5 < 1.15000000000000001e-38

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 55.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if 1.15000000000000001e-38 < y5 < 3.1000000000000001e-12

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 71.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 71.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 86.2%

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

   if 3.1000000000000001e-12 < y5 < 2.40000000000000013e56

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 77.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]
3. Recombined 7 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.8 \cdot 10^{+162}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.25 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -1.4 \cdot 10^{+32}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.28 \cdot 10^{-163}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.2 \cdot 10^{-234}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{+56}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \end{array} \]

Alternative 9: 43.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y5 \leq -4 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-234}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (- (* a (- (* t y2) (* y y3))) (* y0 (- (* k y2) (* j y3)))))))
        (t_2 (- (* c y0) (* a y1))))
   (if (<= y5 -4e+166)
     t_1
     (if (<= y5 -1.8e+116)
       (* c (* x (- (* y0 y2) (* y i))))
       (if (<= y5 -2e+32)
         t_1
         (if (<= y5 2.2e-234)
           (*
            c
            (+
             (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= y5 6.2e-39)
             (*
              x
              (+
               (+ (* y (- (* a b) (* c i))) (* y2 t_2))
               (* j (- (* i y1) (* b y0)))))
             (if (<= y5 1.75e-12)
               (* a (* b (- (* x y) (* z t))))
               (if (<= y5 9.8e+57)
                 (*
                  y2
                  (+
                   (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
                   (* t (- (* a y5) (* c y4)))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y5 <= -4e+166) {
		tmp = t_1;
	} else if (y5 <= -1.8e+116) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -2e+32) {
		tmp = t_1;
	} else if (y5 <= 2.2e-234) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 6.2e-39) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 1.75e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 9.8e+57) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))))
    t_2 = (c * y0) - (a * y1)
    if (y5 <= (-4d+166)) then
        tmp = t_1
    else if (y5 <= (-1.8d+116)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y5 <= (-2d+32)) then
        tmp = t_1
    else if (y5 <= 2.2d-234) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 6.2d-39) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    else if (y5 <= 1.75d-12) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y5 <= 9.8d+57) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	double t_2 = (c * y0) - (a * y1);
	double tmp;
	if (y5 <= -4e+166) {
		tmp = t_1;
	} else if (y5 <= -1.8e+116) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= -2e+32) {
		tmp = t_1;
	} else if (y5 <= 2.2e-234) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 6.2e-39) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	} else if (y5 <= 1.75e-12) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= 9.8e+57) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))))
	t_2 = (c * y0) - (a * y1)
	tmp = 0
	if y5 <= -4e+166:
		tmp = t_1
	elif y5 <= -1.8e+116:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y5 <= -2e+32:
		tmp = t_1
	elif y5 <= 2.2e-234:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 6.2e-39:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	elif y5 <= 1.75e-12:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y5 <= 9.8e+57:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3))))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y5 <= -4e+166)
		tmp = t_1;
	elseif (y5 <= -1.8e+116)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y5 <= -2e+32)
		tmp = t_1;
	elseif (y5 <= 2.2e-234)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 6.2e-39)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y5 <= 1.75e-12)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y5 <= 9.8e+57)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) - (y0 * ((k * y2) - (j * y3)))));
	t_2 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y5 <= -4e+166)
		tmp = t_1;
	elseif (y5 <= -1.8e+116)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y5 <= -2e+32)
		tmp = t_1;
	elseif (y5 <= 2.2e-234)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 6.2e-39)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	elseif (y5 <= 1.75e-12)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y5 <= 9.8e+57)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4e+166], t$95$1, If[LessEqual[y5, -1.8e+116], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2e+32], t$95$1, If[LessEqual[y5, 2.2e-234], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.2e-39], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.75e-12], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.8e+57], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -3.99999999999999976e166 or -1.79999999999999985e116 < y5 < -2.00000000000000011e32 or 9.7999999999999998e57 < y5

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 63.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.2%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 63.2%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 63.2%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if -3.99999999999999976e166 < y5 < -1.79999999999999985e116

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -2.00000000000000011e32 < y5 < 2.1999999999999999e-234

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.8%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 2.1999999999999999e-234 < y5 < 6.1999999999999994e-39

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 55.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if 6.1999999999999994e-39 < y5 < 1.75e-12

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 71.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 71.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 71.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 86.2%

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

   if 1.75e-12 < y5 < 9.7999999999999998e57

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 77.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4 \cdot 10^{+166}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.8 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{+32}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.2 \cdot 10^{-234}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 6.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+57}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \end{array} \]

Alternative 10: 40.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := a \cdot b - c \cdot i\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y5 \cdot \left(i \cdot t_1 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot t_4\right)\right)\\ t_6 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;y4 \leq -2.2 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t_4 - t_1 \cdot b\right) + c \cdot t_6\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_2 + y2 \cdot t_3\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -2.45 \cdot 10^{-117}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_3 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.9 \cdot 10^{-290}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot t_6\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-41}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot t_2\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (* y5 (+ (* i t_1) (- (* a (- (* t y2) (* y y3))) (* y0 t_4)))))
        (t_6 (- (* y y3) (* t y2))))
   (if (<= y4 -2.2e+109)
     (* y4 (+ (- (* y1 t_4) (* t_1 b)) (* c t_6)))
     (if (<= y4 -1.6e-8)
       (* x (+ (+ (* y t_2) (* y2 t_3)) (* j (- (* i y1) (* b y0)))))
       (if (<= y4 -2.45e-117)
         (*
          y2
          (+
           (+ (* x t_3) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y4 -1.9e-290)
           t_5
           (if (<= y4 4.8e-146)
             (*
              c
              (+
               (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
               (* y4 t_6)))
             (if (<= y4 1.9e-41)
               t_5
               (if (<= y4 7.2e+120)
                 (*
                  y
                  (+
                   (+ (* k (- (* i y5) (* b y4))) (* x t_2))
                   (* y3 (- (* c y4) (* a y5)))))
                 (* (* c y4) t_6))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * b) - (c * i);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	double t_6 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -2.2e+109) {
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * t_6));
	} else if (y4 <= -1.6e-8) {
		tmp = x * (((y * t_2) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -2.45e-117) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -1.9e-290) {
		tmp = t_5;
	} else if (y4 <= 4.8e-146) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_6));
	} else if (y4 <= 1.9e-41) {
		tmp = t_5;
	} else if (y4 <= 7.2e+120) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = (c * y4) * t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (a * b) - (c * i)
    t_3 = (c * y0) - (a * y1)
    t_4 = (k * y2) - (j * y3)
    t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)))
    t_6 = (y * y3) - (t * y2)
    if (y4 <= (-2.2d+109)) then
        tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * t_6))
    else if (y4 <= (-1.6d-8)) then
        tmp = x * (((y * t_2) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
    else if (y4 <= (-2.45d-117)) then
        tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y4 <= (-1.9d-290)) then
        tmp = t_5
    else if (y4 <= 4.8d-146) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_6))
    else if (y4 <= 1.9d-41) then
        tmp = t_5
    else if (y4 <= 7.2d+120) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))))
    else
        tmp = (c * y4) * t_6
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * b) - (c * i);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	double t_6 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -2.2e+109) {
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * t_6));
	} else if (y4 <= -1.6e-8) {
		tmp = x * (((y * t_2) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	} else if (y4 <= -2.45e-117) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= -1.9e-290) {
		tmp = t_5;
	} else if (y4 <= 4.8e-146) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_6));
	} else if (y4 <= 1.9e-41) {
		tmp = t_5;
	} else if (y4 <= 7.2e+120) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	} else {
		tmp = (c * y4) * t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (a * b) - (c * i)
	t_3 = (c * y0) - (a * y1)
	t_4 = (k * y2) - (j * y3)
	t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)))
	t_6 = (y * y3) - (t * y2)
	tmp = 0
	if y4 <= -2.2e+109:
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * t_6))
	elif y4 <= -1.6e-8:
		tmp = x * (((y * t_2) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))))
	elif y4 <= -2.45e-117:
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y4 <= -1.9e-290:
		tmp = t_5
	elif y4 <= 4.8e-146:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_6))
	elif y4 <= 1.9e-41:
		tmp = t_5
	elif y4 <= 7.2e+120:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))))
	else:
		tmp = (c * y4) * t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y5 * Float64(Float64(i * t_1) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y0 * t_4))))
	t_6 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (y4 <= -2.2e+109)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_4) - Float64(t_1 * b)) + Float64(c * t_6)));
	elseif (y4 <= -1.6e-8)
		tmp = Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * t_3)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= -2.45e-117)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_3) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y4 <= -1.9e-290)
		tmp = t_5;
	elseif (y4 <= 4.8e-146)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * t_6)));
	elseif (y4 <= 1.9e-41)
		tmp = t_5;
	elseif (y4 <= 7.2e+120)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * t_2)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	else
		tmp = Float64(Float64(c * y4) * t_6);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (a * b) - (c * i);
	t_3 = (c * y0) - (a * y1);
	t_4 = (k * y2) - (j * y3);
	t_5 = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) - (y0 * t_4)));
	t_6 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (y4 <= -2.2e+109)
		tmp = y4 * (((y1 * t_4) - (t_1 * b)) + (c * t_6));
	elseif (y4 <= -1.6e-8)
		tmp = x * (((y * t_2) + (y2 * t_3)) + (j * ((i * y1) - (b * y0))));
	elseif (y4 <= -2.45e-117)
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y4 <= -1.9e-290)
		tmp = t_5;
	elseif (y4 <= 4.8e-146)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * t_6));
	elseif (y4 <= 1.9e-41)
		tmp = t_5;
	elseif (y4 <= 7.2e+120)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * t_2)) + (y3 * ((c * y4) - (a * y5))));
	else
		tmp = (c * y4) * t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(i * t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.2e+109], N[(y4 * N[(N[(N[(y1 * t$95$4), $MachinePrecision] - N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.6e-8], N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.45e-117], N[(y2 * N[(N[(N[(x * t$95$3), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.9e-290], t$95$5, If[LessEqual[y4, 4.8e-146], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.9e-41], t$95$5, If[LessEqual[y4, 7.2e+120], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * y4), $MachinePrecision] * t$95$6), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -2.1999999999999999e109

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 67.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -2.1999999999999999e109 < y4 < -1.6000000000000001e-8

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   if -1.6000000000000001e-8 < y4 < -2.4499999999999999e-117

   1. Initial program 4.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 4.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 4.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 56.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   if -2.4499999999999999e-117 < y4 < -1.89999999999999988e-290 or 4.8000000000000003e-146 < y4 < 1.8999999999999999e-41

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 59.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 59.4%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 59.4%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   if -1.89999999999999988e-290 < y4 < 4.8000000000000003e-146

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 66.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.5%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.8999999999999999e-41 < y4 < 7.20000000000000031e120

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 62.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.5%

         \[\leadsto y \cdot \left(\left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      2. mul-1-neg 62.5%

         \[\leadsto y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 7.20000000000000031e120 < y4

   1. Initial program 7.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 7.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 7.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 58.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.2 \cdot 10^{+109}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -2.45 \cdot 10^{-117}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.9 \cdot 10^{-290}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.8 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-41}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \end{array} \]

Alternative 11: 31.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+160}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+32}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (- (* y1 (- (* k y2) (* j y3))) (* (- (* y k) (* t j)) b))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= a -5.2e+160)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= a -3.25e+63)
       t_1
       (if (<= a -9e+32)
         (* (* y2 y4) (- (* k y1) (* t c)))
         (if (<= a -7e+19)
           (* c (* y (- (* y3 y4) (* x i))))
           (if (<= a -7.8e-241)
             (* b (* y4 (- (* t j) (* y k))))
             (if (<= a -1.6e-307)
               t_1
               (if (<= a 4e-172)
                 (* c (* x (- (* y0 y2) (* y i))))
                 (if (<= a 9.5e-56)
                   (* z (* i (- (* t c) (* k y1))))
                   (if (<= a 2.45e+145)
                     (* a (* y2 (- (* t y5) (* x y1))))
                     (* (* y a) (- (* x b) (* y3 y5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (a <= -5.2e+160) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -3.25e+63) {
		tmp = t_1;
	} else if (a <= -9e+32) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (a <= -7e+19) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= -7.8e-241) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1.6e-307) {
		tmp = t_1;
	} else if (a <= 4e-172) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 9.5e-56) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (a <= 2.45e+145) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))))
    if (a <= (-5.2d+160)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (a <= (-3.25d+63)) then
        tmp = t_1
    else if (a <= (-9d+32)) then
        tmp = (y2 * y4) * ((k * y1) - (t * c))
    else if (a <= (-7d+19)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= (-7.8d-241)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-1.6d-307)) then
        tmp = t_1
    else if (a <= 4d-172) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (a <= 9.5d-56) then
        tmp = z * (i * ((t * c) - (k * y1)))
    else if (a <= 2.45d+145) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else
        tmp = (y * a) * ((x * b) - (y3 * y5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (a <= -5.2e+160) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -3.25e+63) {
		tmp = t_1;
	} else if (a <= -9e+32) {
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	} else if (a <= -7e+19) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= -7.8e-241) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1.6e-307) {
		tmp = t_1;
	} else if (a <= 4e-172) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 9.5e-56) {
		tmp = z * (i * ((t * c) - (k * y1)));
	} else if (a <= 2.45e+145) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if a <= -5.2e+160:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif a <= -3.25e+63:
		tmp = t_1
	elif a <= -9e+32:
		tmp = (y2 * y4) * ((k * y1) - (t * c))
	elif a <= -7e+19:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= -7.8e-241:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -1.6e-307:
		tmp = t_1
	elif a <= 4e-172:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif a <= 9.5e-56:
		tmp = z * (i * ((t * c) - (k * y1)))
	elif a <= 2.45e+145:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	else:
		tmp = (y * a) * ((x * b) - (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(Float64(Float64(y * k) - Float64(t * j)) * b)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (a <= -5.2e+160)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (a <= -3.25e+63)
		tmp = t_1;
	elseif (a <= -9e+32)
		tmp = Float64(Float64(y2 * y4) * Float64(Float64(k * y1) - Float64(t * c)));
	elseif (a <= -7e+19)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= -7.8e-241)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -1.6e-307)
		tmp = t_1;
	elseif (a <= 4e-172)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (a <= 9.5e-56)
		tmp = Float64(z * Float64(i * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (a <= 2.45e+145)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	else
		tmp = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((y1 * ((k * y2) - (j * y3))) - (((y * k) - (t * j)) * b)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (a <= -5.2e+160)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (a <= -3.25e+63)
		tmp = t_1;
	elseif (a <= -9e+32)
		tmp = (y2 * y4) * ((k * y1) - (t * c));
	elseif (a <= -7e+19)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= -7.8e-241)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -1.6e-307)
		tmp = t_1;
	elseif (a <= 4e-172)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (a <= 9.5e-56)
		tmp = z * (i * ((t * c) - (k * y1)));
	elseif (a <= 2.45e+145)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	else
		tmp = (y * a) * ((x * b) - (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+160], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.25e+63], t$95$1, If[LessEqual[a, -9e+32], N[(N[(y2 * y4), $MachinePrecision] * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e+19], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e-241], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-307], t$95$1, If[LessEqual[a, 4e-172], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-56], N[(z * N[(i * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+145], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -5.2000000000000001e160

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y5 around inf 66.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot \left(y5 \cdot y2\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 69.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y5\right) \cdot y2} \]

      2. *-commutative 69.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right)\right)} \cdot y2 \]

      3. associate-*l* 66.0%

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y2\right)} \]

      4. cancel-sign-sub-inv 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + \left(--1\right) \cdot \left(a \cdot t\right)\right)} \cdot y2\right) \]

      5. metadata-eval 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{1} \cdot \left(a \cdot t\right)\right) \cdot y2\right) \]

      6. *-lft-identity 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{a \cdot t}\right) \cdot y2\right) \]

      7. +-commutative 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t + -1 \cdot \left(k \cdot y0\right)\right)} \cdot y2\right) \]

      8. mul-1-neg 66.0%

         \[\leadsto y5 \cdot \left(\left(a \cdot t + \color{blue}{\left(-k \cdot y0\right)}\right) \cdot y2\right) \]

      9. unsub-neg 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t - k \cdot y0\right)} \cdot y2\right) \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{y5 \cdot \left(\left(a \cdot t - k \cdot y0\right) \cdot y2\right)} \]

   if -5.2000000000000001e160 < a < -3.24999999999999996e63 or -7.7999999999999998e-241 < a < -1.60000000000000005e-307

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.24999999999999996e63 < a < -9.0000000000000007e32

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 68.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.0%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 68.0%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 68.0%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   if -9.0000000000000007e32 < a < -7e19

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 80.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 80.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 80.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y around -inf 100.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 100.0%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 100.0%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 100.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if -7e19 < a < -7.7999999999999998e-241

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 41.2%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   if -1.60000000000000005e-307 < a < 4.0000000000000002e-172

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if 4.0000000000000002e-172 < a < 9.4999999999999991e-56

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 36.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in i around inf 45.4%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot \left(i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot i\right) \cdot z\right)} \]

      2. distribute-lft-out-- 52.9%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(c \cdot t - k \cdot y1\right)\right)} \cdot i\right) \cdot z\right) \]

      3. associate-*r* 52.9%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-1 \cdot \left(\left(c \cdot t - k \cdot y1\right) \cdot i\right)\right)} \cdot z\right) \]

      4. mul-1-neg 52.9%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-\left(c \cdot t - k \cdot y1\right) \cdot i\right)} \cdot z\right) \]

      5. *-commutative 52.9%

         \[\leadsto -1 \cdot \left(\left(-\color{blue}{i \cdot \left(c \cdot t - k \cdot y1\right)}\right) \cdot z\right) \]

      6. *-commutative 52.9%

         \[\leadsto -1 \cdot \left(\left(-i \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \cdot z\right) \]

   7. Simplified 52.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-i \cdot \left(t \cdot c - k \cdot y1\right)\right) \cdot z\right)} \]

   if 9.4999999999999991e-56 < a < 2.45000000000000001e145

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if 2.45000000000000001e145 < a

   1. Initial program 9.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 52.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 52.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 52.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 52.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 67.1%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. +-commutative 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      4. mul-1-neg 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      5. unsub-neg 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      6. *-commutative 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x - \color{blue}{y5 \cdot y3}\right) \]

   9. Simplified 67.1%

      \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x - y5 \cdot y3\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+160}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{+63}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+32}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-307}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - \left(y \cdot k - t \cdot j\right) \cdot b\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \]

Alternative 12: 31.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ t_3 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+211}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-250}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-85}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* c (* i (- (* z t) (* x y)))))
        (t_3 (* c (* x (- (* y0 y2) (* y i))))))
   (if (<= x -3.6e+211)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= x -4.1e+99)
       (* a (* b (- (* x y) (* z t))))
       (if (<= x -2.45e+38)
         t_3
         (if (<= x -1.55e+26)
           (* c (* (* t y2) (- y4)))
           (if (<= x -4.3e-178)
             (* t (* y2 (- (* a y5) (* c y4))))
             (if (<= x 1.85e-250)
               (* y4 (* y1 (- (* k y2) (* j y3))))
               (if (<= x 1.75e-176)
                 t_1
                 (if (<= x 1.2e-118)
                   t_2
                   (if (<= x 1.3e-85)
                     (* y1 (* a (- (* z y3) (* x y2))))
                     (if (<= x 2.6e-62)
                       (* c (* y (- (* y3 y4) (* x i))))
                       (if (<= x 2e-40)
                         t_2
                         (if (<= x 6.5e+125) t_1 t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (i * ((z * t) - (x * y)));
	double t_3 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -3.6e+211) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -4.1e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -2.45e+38) {
		tmp = t_3;
	} else if (x <= -1.55e+26) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= -4.3e-178) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.85e-250) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (x <= 1.75e-176) {
		tmp = t_1;
	} else if (x <= 1.2e-118) {
		tmp = t_2;
	} else if (x <= 1.3e-85) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 2.6e-62) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (x <= 2e-40) {
		tmp = t_2;
	} else if (x <= 6.5e+125) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = c * (i * ((z * t) - (x * y)))
    t_3 = c * (x * ((y0 * y2) - (y * i)))
    if (x <= (-3.6d+211)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (x <= (-4.1d+99)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-2.45d+38)) then
        tmp = t_3
    else if (x <= (-1.55d+26)) then
        tmp = c * ((t * y2) * -y4)
    else if (x <= (-4.3d-178)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 1.85d-250) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (x <= 1.75d-176) then
        tmp = t_1
    else if (x <= 1.2d-118) then
        tmp = t_2
    else if (x <= 1.3d-85) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (x <= 2.6d-62) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (x <= 2d-40) then
        tmp = t_2
    else if (x <= 6.5d+125) then
        tmp = t_1
    else
        tmp = t_3
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (i * ((z * t) - (x * y)));
	double t_3 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -3.6e+211) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -4.1e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -2.45e+38) {
		tmp = t_3;
	} else if (x <= -1.55e+26) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= -4.3e-178) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.85e-250) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (x <= 1.75e-176) {
		tmp = t_1;
	} else if (x <= 1.2e-118) {
		tmp = t_2;
	} else if (x <= 1.3e-85) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 2.6e-62) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (x <= 2e-40) {
		tmp = t_2;
	} else if (x <= 6.5e+125) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = c * (i * ((z * t) - (x * y)))
	t_3 = c * (x * ((y0 * y2) - (y * i)))
	tmp = 0
	if x <= -3.6e+211:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif x <= -4.1e+99:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -2.45e+38:
		tmp = t_3
	elif x <= -1.55e+26:
		tmp = c * ((t * y2) * -y4)
	elif x <= -4.3e-178:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 1.85e-250:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif x <= 1.75e-176:
		tmp = t_1
	elif x <= 1.2e-118:
		tmp = t_2
	elif x <= 1.3e-85:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif x <= 2.6e-62:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif x <= 2e-40:
		tmp = t_2
	elif x <= 6.5e+125:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))))
	t_3 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	tmp = 0.0
	if (x <= -3.6e+211)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (x <= -4.1e+99)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -2.45e+38)
		tmp = t_3;
	elseif (x <= -1.55e+26)
		tmp = Float64(c * Float64(Float64(t * y2) * Float64(-y4)));
	elseif (x <= -4.3e-178)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 1.85e-250)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 1.75e-176)
		tmp = t_1;
	elseif (x <= 1.2e-118)
		tmp = t_2;
	elseif (x <= 1.3e-85)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (x <= 2.6e-62)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (x <= 2e-40)
		tmp = t_2;
	elseif (x <= 6.5e+125)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = c * (i * ((z * t) - (x * y)));
	t_3 = c * (x * ((y0 * y2) - (y * i)));
	tmp = 0.0;
	if (x <= -3.6e+211)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (x <= -4.1e+99)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -2.45e+38)
		tmp = t_3;
	elseif (x <= -1.55e+26)
		tmp = c * ((t * y2) * -y4);
	elseif (x <= -4.3e-178)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 1.85e-250)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (x <= 1.75e-176)
		tmp = t_1;
	elseif (x <= 1.2e-118)
		tmp = t_2;
	elseif (x <= 1.3e-85)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (x <= 2.6e-62)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (x <= 2e-40)
		tmp = t_2;
	elseif (x <= 6.5e+125)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+211], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.1e+99], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.45e+38], t$95$3, If[LessEqual[x, -1.55e+26], N[(c * N[(N[(t * y2), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e-178], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-250], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-176], t$95$1, If[LessEqual[x, 1.2e-118], t$95$2, If[LessEqual[x, 1.3e-85], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-62], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-40], t$95$2, If[LessEqual[x, 6.5e+125], t$95$1, t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -3.60000000000000003e211

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y2 around inf 62.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -3.60000000000000003e211 < x < -4.09999999999999979e99

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 65.8%

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

   if -4.09999999999999979e99 < x < -2.45000000000000001e38 or 6.4999999999999999e125 < x

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -2.45000000000000001e38 < x < -1.55e26

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 34.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.3%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 34.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 34.3%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 67.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

   10. Simplified 67.4%

       \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

   if -1.55e26 < x < -4.3e-178

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 50.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 50.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around inf 48.1%

      \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot y2\right)} \]

   if -4.3e-178 < x < 1.8499999999999999e-250

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 44.5%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   if 1.8499999999999999e-250 < x < 1.75e-176 or 1.9999999999999999e-40 < x < 6.4999999999999999e125

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 1.75e-176 < x < 1.2000000000000001e-118 or 2.5999999999999999e-62 < x < 1.9999999999999999e-40

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 58.7%

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

   if 1.2000000000000001e-118 < x < 1.30000000000000006e-85

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y1 around inf 51.8%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if 1.30000000000000006e-85 < x < 2.5999999999999999e-62

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 12.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 75.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 75.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 75.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y around -inf 63.8%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 63.8%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 63.8%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 63.8%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 63.8%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+211}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-250}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-85}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 13: 30.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-257}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;\left(-b\right) \cdot \left(\left(y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i)))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= x -2.4e+212)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= x -1.35e+99)
       (* a (* b (- (* x y) (* z t))))
       (if (<= x -6.1e+38)
         t_1
         (if (<= x -2.05e+30)
           (* c (* (* t y2) (- y4)))
           (if (<= x 6.2e-306)
             (* t (* y2 (- (* a y5) (* c y4))))
             (if (<= x 5.4e-257)
               (* (* k y2) (* y1 y4))
               (if (<= x 8e-190)
                 t_2
                 (if (<= x 2.2e-174)
                   (* (- b) (* (* y k) y4))
                   (if (<= x 2.4e-40)
                     (* c (* i (- (* z t) (* x y))))
                     (if (<= x 2.3e+127) t_2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (x <= -2.4e+212) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -1.35e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -6.1e+38) {
		tmp = t_1;
	} else if (x <= -2.05e+30) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= 6.2e-306) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 5.4e-257) {
		tmp = (k * y2) * (y1 * y4);
	} else if (x <= 8e-190) {
		tmp = t_2;
	} else if (x <= 2.2e-174) {
		tmp = -b * ((y * k) * y4);
	} else if (x <= 2.4e-40) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.3e+127) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (x <= (-2.4d+212)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (x <= (-1.35d+99)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-6.1d+38)) then
        tmp = t_1
    else if (x <= (-2.05d+30)) then
        tmp = c * ((t * y2) * -y4)
    else if (x <= 6.2d-306) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 5.4d-257) then
        tmp = (k * y2) * (y1 * y4)
    else if (x <= 8d-190) then
        tmp = t_2
    else if (x <= 2.2d-174) then
        tmp = -b * ((y * k) * y4)
    else if (x <= 2.4d-40) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 2.3d+127) then
        tmp = t_2
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (x <= -2.4e+212) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -1.35e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -6.1e+38) {
		tmp = t_1;
	} else if (x <= -2.05e+30) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= 6.2e-306) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 5.4e-257) {
		tmp = (k * y2) * (y1 * y4);
	} else if (x <= 8e-190) {
		tmp = t_2;
	} else if (x <= 2.2e-174) {
		tmp = -b * ((y * k) * y4);
	} else if (x <= 2.4e-40) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 2.3e+127) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * ((y0 * y2) - (y * i)))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if x <= -2.4e+212:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif x <= -1.35e+99:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -6.1e+38:
		tmp = t_1
	elif x <= -2.05e+30:
		tmp = c * ((t * y2) * -y4)
	elif x <= 6.2e-306:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 5.4e-257:
		tmp = (k * y2) * (y1 * y4)
	elif x <= 8e-190:
		tmp = t_2
	elif x <= 2.2e-174:
		tmp = -b * ((y * k) * y4)
	elif x <= 2.4e-40:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 2.3e+127:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (x <= -2.4e+212)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (x <= -1.35e+99)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -6.1e+38)
		tmp = t_1;
	elseif (x <= -2.05e+30)
		tmp = Float64(c * Float64(Float64(t * y2) * Float64(-y4)));
	elseif (x <= 6.2e-306)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 5.4e-257)
		tmp = Float64(Float64(k * y2) * Float64(y1 * y4));
	elseif (x <= 8e-190)
		tmp = t_2;
	elseif (x <= 2.2e-174)
		tmp = Float64(Float64(-b) * Float64(Float64(y * k) * y4));
	elseif (x <= 2.4e-40)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 2.3e+127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * ((y0 * y2) - (y * i)));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (x <= -2.4e+212)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (x <= -1.35e+99)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -6.1e+38)
		tmp = t_1;
	elseif (x <= -2.05e+30)
		tmp = c * ((t * y2) * -y4);
	elseif (x <= 6.2e-306)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 5.4e-257)
		tmp = (k * y2) * (y1 * y4);
	elseif (x <= 8e-190)
		tmp = t_2;
	elseif (x <= 2.2e-174)
		tmp = -b * ((y * k) * y4);
	elseif (x <= 2.4e-40)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 2.3e+127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+212], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e+99], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.1e+38], t$95$1, If[LessEqual[x, -2.05e+30], N[(c * N[(N[(t * y2), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-306], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e-257], N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-190], t$95$2, If[LessEqual[x, 2.2e-174], N[((-b) * N[(N[(y * k), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-40], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+127], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -2.4e212

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y2 around inf 62.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -2.4e212 < x < -1.34999999999999994e99

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 65.8%

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

   if -1.34999999999999994e99 < x < -6.0999999999999999e38 or 2.3000000000000002e127 < x

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -6.0999999999999999e38 < x < -2.05000000000000003e30

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 34.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.3%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 34.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 34.3%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 67.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

   10. Simplified 67.4%

       \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

   if -2.05000000000000003e30 < x < 6.19999999999999995e-306

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 48.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 48.1%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in y2 around inf 43.3%

      \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y5 - c \cdot y4\right) \cdot y2\right)} \]

   if 6.19999999999999995e-306 < x < 5.3999999999999997e-257

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 23.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 36.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.6%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 46.6%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 46.6%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around inf 38.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. associate-*r* 48.2%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \cdot k \]

      3. associate-*l* 56.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y1\right) \cdot \left(y2 \cdot k\right)} \]

      4. *-commutative 56.9%

         \[\leadsto \left(y4 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y2\right)} \]

      5. *-commutative 56.9%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right)} \cdot \left(k \cdot y2\right) \]

   10. Simplified 56.9%

       \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2\right)} \]

   if 5.3999999999999997e-257 < x < 8.0000000000000002e-190 or 2.39999999999999991e-40 < x < 2.3000000000000002e127

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 39.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 39.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 8.0000000000000002e-190 < x < 2.20000000000000022e-174

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 50.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 63.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 51.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 75.8%

      \[\leadsto \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y\right)\right)}\right) \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 75.8%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(-k \cdot y\right)}\right) \cdot b \]

      2. distribute-lft-neg-out 75.8%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(\left(-k\right) \cdot y\right)}\right) \cdot b \]

      3. *-commutative 75.8%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \cdot b \]

   10. Simplified 75.8%

       \[\leadsto \left(y4 \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \cdot b \]

   if 2.20000000000000022e-174 < x < 2.39999999999999991e-40

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 47.9%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -6.1 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-257}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;\left(-b\right) \cdot \left(\left(y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 14: 27.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_3 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-252}:\\ \;\;\;\;\left(k \cdot \left(i \cdot y1\right)\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+261}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4)))))
        (t_3 (* c (* i (- (* z t) (* x y))))))
   (if (<= x -7e+213)
     t_2
     (if (<= x -1.6e-13)
       (* a (* b (- (* x y) (* z t))))
       (if (<= x -3.4e-155)
         (* a (* y2 (- (* t y5) (* x y1))))
         (if (<= x 1.06e-252)
           (* (* k (* i y1)) (- z))
           (if (<= x 1.55e-176)
             t_1
             (if (<= x 3.1e-40)
               t_3
               (if (<= x 1.46e+127)
                 t_1
                 (if (<= x 5.8e+157)
                   t_2
                   (if (<= x 1.3e+261)
                     (* c (* y (- (* y3 y4) (* x i))))
                     t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = c * (i * ((z * t) - (x * y)));
	double tmp;
	if (x <= -7e+213) {
		tmp = t_2;
	} else if (x <= -1.6e-13) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -3.4e-155) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (x <= 1.06e-252) {
		tmp = (k * (i * y1)) * -z;
	} else if (x <= 1.55e-176) {
		tmp = t_1;
	} else if (x <= 3.1e-40) {
		tmp = t_3;
	} else if (x <= 1.46e+127) {
		tmp = t_1;
	} else if (x <= 5.8e+157) {
		tmp = t_2;
	} else if (x <= 1.3e+261) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    t_3 = c * (i * ((z * t) - (x * y)))
    if (x <= (-7d+213)) then
        tmp = t_2
    else if (x <= (-1.6d-13)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-3.4d-155)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (x <= 1.06d-252) then
        tmp = (k * (i * y1)) * -z
    else if (x <= 1.55d-176) then
        tmp = t_1
    else if (x <= 3.1d-40) then
        tmp = t_3
    else if (x <= 1.46d+127) then
        tmp = t_1
    else if (x <= 5.8d+157) then
        tmp = t_2
    else if (x <= 1.3d+261) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else
        tmp = t_3
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double t_3 = c * (i * ((z * t) - (x * y)));
	double tmp;
	if (x <= -7e+213) {
		tmp = t_2;
	} else if (x <= -1.6e-13) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -3.4e-155) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (x <= 1.06e-252) {
		tmp = (k * (i * y1)) * -z;
	} else if (x <= 1.55e-176) {
		tmp = t_1;
	} else if (x <= 3.1e-40) {
		tmp = t_3;
	} else if (x <= 1.46e+127) {
		tmp = t_1;
	} else if (x <= 5.8e+157) {
		tmp = t_2;
	} else if (x <= 1.3e+261) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	t_3 = c * (i * ((z * t) - (x * y)))
	tmp = 0
	if x <= -7e+213:
		tmp = t_2
	elif x <= -1.6e-13:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -3.4e-155:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif x <= 1.06e-252:
		tmp = (k * (i * y1)) * -z
	elif x <= 1.55e-176:
		tmp = t_1
	elif x <= 3.1e-40:
		tmp = t_3
	elif x <= 1.46e+127:
		tmp = t_1
	elif x <= 5.8e+157:
		tmp = t_2
	elif x <= 1.3e+261:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	t_3 = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))))
	tmp = 0.0
	if (x <= -7e+213)
		tmp = t_2;
	elseif (x <= -1.6e-13)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -3.4e-155)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (x <= 1.06e-252)
		tmp = Float64(Float64(k * Float64(i * y1)) * Float64(-z));
	elseif (x <= 1.55e-176)
		tmp = t_1;
	elseif (x <= 3.1e-40)
		tmp = t_3;
	elseif (x <= 1.46e+127)
		tmp = t_1;
	elseif (x <= 5.8e+157)
		tmp = t_2;
	elseif (x <= 1.3e+261)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	t_3 = c * (i * ((z * t) - (x * y)));
	tmp = 0.0;
	if (x <= -7e+213)
		tmp = t_2;
	elseif (x <= -1.6e-13)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -3.4e-155)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (x <= 1.06e-252)
		tmp = (k * (i * y1)) * -z;
	elseif (x <= 1.55e-176)
		tmp = t_1;
	elseif (x <= 3.1e-40)
		tmp = t_3;
	elseif (x <= 1.46e+127)
		tmp = t_1;
	elseif (x <= 5.8e+157)
		tmp = t_2;
	elseif (x <= 1.3e+261)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+213], t$95$2, If[LessEqual[x, -1.6e-13], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-155], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e-252], N[(N[(k * N[(i * y1), $MachinePrecision]), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[x, 1.55e-176], t$95$1, If[LessEqual[x, 3.1e-40], t$95$3, If[LessEqual[x, 1.46e+127], t$95$1, If[LessEqual[x, 5.8e+157], t$95$2, If[LessEqual[x, 1.3e+261], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -6.9999999999999994e213 or 1.45999999999999997e127 < x < 5.79999999999999975e157

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y2 around inf 67.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -6.9999999999999994e213 < x < -1.6e-13

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 51.5%

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

   if -1.6e-13 < x < -3.4e-155

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if -3.4e-155 < x < 1.06e-252

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 44.3%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 34.2%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right)} \cdot z\right) \]

   if 1.06e-252 < x < 1.54999999999999996e-176 or 3.10000000000000011e-40 < x < 1.45999999999999997e127

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 43.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 43.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 43.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 49.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 1.54999999999999996e-176 < x < 3.10000000000000011e-40 or 1.29999999999999991e261 < x

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 51.0%

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

   if 5.79999999999999975e157 < x < 1.29999999999999991e261

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y around -inf 61.4%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.4%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 61.4%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 61.4%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 61.4%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-252}:\\ \;\;\;\;\left(k \cdot \left(i \cdot y1\right)\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+261}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \]

Alternative 15: 31.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+215}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-250}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* c (* x (- (* y0 y2) (* y i))))))
   (if (<= x -6.5e+215)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= x -2.3e+99)
       (* a (* b (- (* x y) (* z t))))
       (if (<= x -4.3e+38)
         t_2
         (if (<= x -3e+29)
           (* c (* (* t y2) (- y4)))
           (if (<= x -2.8e-178)
             (* (* t j) (- (* b y4) (* i y5)))
             (if (<= x 1.85e-250)
               (* y4 (* y1 (- (* k y2) (* j y3))))
               (if (<= x 7e-175)
                 t_1
                 (if (<= x 9.5e-41)
                   (* c (* i (- (* z t) (* x y))))
                   (if (<= x 4e+125) t_1 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -6.5e+215) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -2.3e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -4.3e+38) {
		tmp = t_2;
	} else if (x <= -3e+29) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= -2.8e-178) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 1.85e-250) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (x <= 7e-175) {
		tmp = t_1;
	} else if (x <= 9.5e-41) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 4e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = c * (x * ((y0 * y2) - (y * i)))
    if (x <= (-6.5d+215)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (x <= (-2.3d+99)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-4.3d+38)) then
        tmp = t_2
    else if (x <= (-3d+29)) then
        tmp = c * ((t * y2) * -y4)
    else if (x <= (-2.8d-178)) then
        tmp = (t * j) * ((b * y4) - (i * y5))
    else if (x <= 1.85d-250) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (x <= 7d-175) then
        tmp = t_1
    else if (x <= 9.5d-41) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 4d+125) then
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -6.5e+215) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -2.3e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -4.3e+38) {
		tmp = t_2;
	} else if (x <= -3e+29) {
		tmp = c * ((t * y2) * -y4);
	} else if (x <= -2.8e-178) {
		tmp = (t * j) * ((b * y4) - (i * y5));
	} else if (x <= 1.85e-250) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (x <= 7e-175) {
		tmp = t_1;
	} else if (x <= 9.5e-41) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 4e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = c * (x * ((y0 * y2) - (y * i)))
	tmp = 0
	if x <= -6.5e+215:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif x <= -2.3e+99:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -4.3e+38:
		tmp = t_2
	elif x <= -3e+29:
		tmp = c * ((t * y2) * -y4)
	elif x <= -2.8e-178:
		tmp = (t * j) * ((b * y4) - (i * y5))
	elif x <= 1.85e-250:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif x <= 7e-175:
		tmp = t_1
	elif x <= 9.5e-41:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 4e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	tmp = 0.0
	if (x <= -6.5e+215)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (x <= -2.3e+99)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -4.3e+38)
		tmp = t_2;
	elseif (x <= -3e+29)
		tmp = Float64(c * Float64(Float64(t * y2) * Float64(-y4)));
	elseif (x <= -2.8e-178)
		tmp = Float64(Float64(t * j) * Float64(Float64(b * y4) - Float64(i * y5)));
	elseif (x <= 1.85e-250)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 7e-175)
		tmp = t_1;
	elseif (x <= 9.5e-41)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 4e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = c * (x * ((y0 * y2) - (y * i)));
	tmp = 0.0;
	if (x <= -6.5e+215)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (x <= -2.3e+99)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -4.3e+38)
		tmp = t_2;
	elseif (x <= -3e+29)
		tmp = c * ((t * y2) * -y4);
	elseif (x <= -2.8e-178)
		tmp = (t * j) * ((b * y4) - (i * y5));
	elseif (x <= 1.85e-250)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (x <= 7e-175)
		tmp = t_1;
	elseif (x <= 9.5e-41)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 4e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+215], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e+99], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e+38], t$95$2, If[LessEqual[x, -3e+29], N[(c * N[(N[(t * y2), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-178], N[(N[(t * j), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-250], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-175], t$95$1, If[LessEqual[x, 9.5e-41], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+125], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -6.4999999999999997e215

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y2 around inf 62.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -6.4999999999999997e215 < x < -2.30000000000000019e99

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 65.8%

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

   if -2.30000000000000019e99 < x < -4.2999999999999997e38 or 3.9999999999999997e125 < x

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -4.2999999999999997e38 < x < -2.9999999999999999e29

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 34.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.3%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 34.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 34.3%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 67.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

   10. Simplified 67.4%

       \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

   if -2.9999999999999999e29 < x < -2.80000000000000019e-178

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 50.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 50.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in j around inf 53.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot \left(y4 \cdot b - i \cdot y5\right)} \]

      2. *-commutative 53.7%

         \[\leadsto \color{blue}{\left(y4 \cdot b - i \cdot y5\right) \cdot \left(t \cdot j\right)} \]

   9. Simplified 53.7%

      \[\leadsto \color{blue}{\left(y4 \cdot b - i \cdot y5\right) \cdot \left(t \cdot j\right)} \]

   if -2.80000000000000019e-178 < x < 1.8499999999999999e-250

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 44.5%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   if 1.8499999999999999e-250 < x < 6.99999999999999997e-175 or 9.4999999999999997e-41 < x < 3.9999999999999997e125

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 6.99999999999999997e-175 < x < 9.4999999999999997e-41

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 48.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 46.5%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+215}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-250}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 16: 28.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -9 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-272}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.1 \cdot 10^{-34}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;k \leq 1.04 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y5\right) \cdot \left(j \cdot y3 - k \cdot y2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -1.75e+76)
   (* b (* y4 (- (* t j) (* y k))))
   (if (<= k -8.5e-92)
     (* z (* a (- (* y1 y3) (* t b))))
     (if (<= k -1.6e-206)
       (* a (* y5 (- (* t y2) (* y y3))))
       (if (<= k -9e-241)
         (* c (* i (- (* z t) (* x y))))
         (if (<= k -1.35e-272)
           (* y2 (* c (- (* x y0) (* t y4))))
           (if (<= k 6.1e-34)
             (* (* t y5) (- (* a y2) (* i j)))
             (if (<= k 1.04e+34)
               (* (* y a) (- (* x b) (* y3 y5)))
               (if (<= k 4.4e+67)
                 (* y5 (* y2 (- (* t a) (* k y0))))
                 (if (<= k 8.5e+146)
                   (* y4 (* y2 (* k y1)))
                   (* (* y0 y5) (- (* j y3) (* k y2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -1.75e+76) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= -8.5e-92) {
		tmp = z * (a * ((y1 * y3) - (t * b)));
	} else if (k <= -1.6e-206) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= -9e-241) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (k <= -1.35e-272) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (k <= 6.1e-34) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (k <= 1.04e+34) {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	} else if (k <= 4.4e+67) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (k <= 8.5e+146) {
		tmp = y4 * (y2 * (k * y1));
	} else {
		tmp = (y0 * y5) * ((j * y3) - (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-1.75d+76)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (k <= (-8.5d-92)) then
        tmp = z * (a * ((y1 * y3) - (t * b)))
    else if (k <= (-1.6d-206)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (k <= (-9d-241)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (k <= (-1.35d-272)) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (k <= 6.1d-34) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (k <= 1.04d+34) then
        tmp = (y * a) * ((x * b) - (y3 * y5))
    else if (k <= 4.4d+67) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (k <= 8.5d+146) then
        tmp = y4 * (y2 * (k * y1))
    else
        tmp = (y0 * y5) * ((j * y3) - (k * y2))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -1.75e+76) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (k <= -8.5e-92) {
		tmp = z * (a * ((y1 * y3) - (t * b)));
	} else if (k <= -1.6e-206) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (k <= -9e-241) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (k <= -1.35e-272) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (k <= 6.1e-34) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (k <= 1.04e+34) {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	} else if (k <= 4.4e+67) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (k <= 8.5e+146) {
		tmp = y4 * (y2 * (k * y1));
	} else {
		tmp = (y0 * y5) * ((j * y3) - (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -1.75e+76:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif k <= -8.5e-92:
		tmp = z * (a * ((y1 * y3) - (t * b)))
	elif k <= -1.6e-206:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif k <= -9e-241:
		tmp = c * (i * ((z * t) - (x * y)))
	elif k <= -1.35e-272:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif k <= 6.1e-34:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif k <= 1.04e+34:
		tmp = (y * a) * ((x * b) - (y3 * y5))
	elif k <= 4.4e+67:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif k <= 8.5e+146:
		tmp = y4 * (y2 * (k * y1))
	else:
		tmp = (y0 * y5) * ((j * y3) - (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -1.75e+76)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (k <= -8.5e-92)
		tmp = Float64(z * Float64(a * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (k <= -1.6e-206)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (k <= -9e-241)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (k <= -1.35e-272)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (k <= 6.1e-34)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (k <= 1.04e+34)
		tmp = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)));
	elseif (k <= 4.4e+67)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (k <= 8.5e+146)
		tmp = Float64(y4 * Float64(y2 * Float64(k * y1)));
	else
		tmp = Float64(Float64(y0 * y5) * Float64(Float64(j * y3) - Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -1.75e+76)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (k <= -8.5e-92)
		tmp = z * (a * ((y1 * y3) - (t * b)));
	elseif (k <= -1.6e-206)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (k <= -9e-241)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (k <= -1.35e-272)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (k <= 6.1e-34)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (k <= 1.04e+34)
		tmp = (y * a) * ((x * b) - (y3 * y5));
	elseif (k <= 4.4e+67)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (k <= 8.5e+146)
		tmp = y4 * (y2 * (k * y1));
	else
		tmp = (y0 * y5) * ((j * y3) - (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -1.75e+76], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -8.5e-92], N[(z * N[(a * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.6e-206], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9e-241], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.35e-272], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.1e-34], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.04e+34], N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.4e+67], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.5e+146], N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y0 * y5), $MachinePrecision] * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -1.75e76

   1. Initial program 15.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 57.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 59.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   if -1.75e76 < k < -8.50000000000000067e-92

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in a around inf 43.7%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot z\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto -1 \cdot \left(\left(a \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \cdot z\right) \]

      2. sub-neg 43.7%

         \[\leadsto -1 \cdot \left(\left(a \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \cdot z\right) \]

      3. *-commutative 43.7%

         \[\leadsto -1 \cdot \left(\left(a \cdot \left(t \cdot b - \color{blue}{y3 \cdot y1}\right)\right) \cdot z\right) \]

   7. Simplified 43.7%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot \left(t \cdot b - y3 \cdot y1\right)\right)} \cdot z\right) \]

   if -8.50000000000000067e-92 < k < -1.59999999999999988e-206

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 56.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -1.59999999999999988e-206 < k < -8.9999999999999997e-241

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 12.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 87.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 87.3%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 87.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 87.3%

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

   if -8.9999999999999997e-241 < k < -1.34999999999999996e-272

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 64.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 72.8%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if -1.34999999999999996e-272 < k < 6.0999999999999998e-34

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 57.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.3%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 57.3%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 57.3%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around inf 46.2%

      \[\leadsto -\color{blue}{\left(i \cdot j - a \cdot y2\right) \cdot \left(t \cdot y5\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto -\left(\color{blue}{j \cdot i} - a \cdot y2\right) \cdot \left(t \cdot y5\right) \]

      2. *-commutative 46.2%

         \[\leadsto -\left(j \cdot i - \color{blue}{y2 \cdot a}\right) \cdot \left(t \cdot y5\right) \]

      3. *-commutative 46.2%

         \[\leadsto -\left(j \cdot i - y2 \cdot a\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   9. Simplified 46.2%

      \[\leadsto -\color{blue}{\left(j \cdot i - y2 \cdot a\right) \cdot \left(y5 \cdot t\right)} \]

   if 6.0999999999999998e-34 < k < 1.0399999999999999e34

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 72.7%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 72.7%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. +-commutative 72.7%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      4. mul-1-neg 72.7%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      5. unsub-neg 72.7%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      6. *-commutative 72.7%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x - \color{blue}{y5 \cdot y3}\right) \]

   9. Simplified 72.7%

      \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x - y5 \cdot y3\right)} \]

   if 1.0399999999999999e34 < k < 4.4e67

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 40.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 60.0%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y5 around inf 82.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot \left(y5 \cdot y2\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 82.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y5\right) \cdot y2} \]

      2. *-commutative 82.4%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right)\right)} \cdot y2 \]

      3. associate-*l* 100.0%

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y2\right)} \]

      4. cancel-sign-sub-inv 100.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + \left(--1\right) \cdot \left(a \cdot t\right)\right)} \cdot y2\right) \]

      5. metadata-eval 100.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{1} \cdot \left(a \cdot t\right)\right) \cdot y2\right) \]

      6. *-lft-identity 100.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{a \cdot t}\right) \cdot y2\right) \]

      7. +-commutative 100.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t + -1 \cdot \left(k \cdot y0\right)\right)} \cdot y2\right) \]

      8. mul-1-neg 100.0%

         \[\leadsto y5 \cdot \left(\left(a \cdot t + \color{blue}{\left(-k \cdot y0\right)}\right) \cdot y2\right) \]

      9. unsub-neg 100.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t - k \cdot y0\right)} \cdot y2\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{y5 \cdot \left(\left(a \cdot t - k \cdot y0\right) \cdot y2\right)} \]

   if 4.4e67 < k < 8.5e146

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 50.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 50.3%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 50.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 45.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto k \cdot \color{blue}{\left(\left(y1 \cdot y2\right) \cdot y4\right)} \]

      2. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right) \cdot y4} \]

      3. associate-*r* 63.0%

         \[\leadsto \color{blue}{\left(\left(k \cdot y1\right) \cdot y2\right)} \cdot y4 \]

      4. *-commutative 63.0%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(k \cdot y1\right)\right)} \cdot y4 \]

      5. *-commutative 63.0%

         \[\leadsto \left(y2 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \cdot y4 \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{\left(y2 \cdot \left(y1 \cdot k\right)\right) \cdot y4} \]

   if 8.5e146 < k

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 43.5%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around inf 44.0%

      \[\leadsto -\color{blue}{y0 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto -\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right)} \]

      2. *-commutative 44.0%

         \[\leadsto -\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \]

   9. Simplified 44.0%

      \[\leadsto -\color{blue}{\left(y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;k \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -9 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-272}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.1 \cdot 10^{-34}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;k \leq 1.04 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+146}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y5\right) \cdot \left(j \cdot y3 - k \cdot y2\right)\\ \end{array} \]

Alternative 17: 30.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(y4 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* c (* x (- (* y0 y2) (* y i))))))
   (if (<= x -2.35e+213)
     (* c (* y2 (- (* x y0) (* t y4))))
     (if (<= x -2.1e+99)
       (* a (* b (- (* x y) (* z t))))
       (if (<= x -6.5e+37)
         t_2
         (if (<= x -6.8e-13)
           (* (* t c) (* y4 (- y2)))
           (if (<= x -1e-151)
             (* a (* y2 (- (* t y5) (* x y1))))
             (if (<= x 7e-176)
               t_1
               (if (<= x 1.6e-40)
                 (* c (* i (- (* z t) (* x y))))
                 (if (<= x 3.05e+125) t_1 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -2.35e+213) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -2.1e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -6.5e+37) {
		tmp = t_2;
	} else if (x <= -6.8e-13) {
		tmp = (t * c) * (y4 * -y2);
	} else if (x <= -1e-151) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (x <= 7e-176) {
		tmp = t_1;
	} else if (x <= 1.6e-40) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 3.05e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = c * (x * ((y0 * y2) - (y * i)))
    if (x <= (-2.35d+213)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (x <= (-2.1d+99)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-6.5d+37)) then
        tmp = t_2
    else if (x <= (-6.8d-13)) then
        tmp = (t * c) * (y4 * -y2)
    else if (x <= (-1d-151)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (x <= 7d-176) then
        tmp = t_1
    else if (x <= 1.6d-40) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (x <= 3.05d+125) then
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = c * (x * ((y0 * y2) - (y * i)));
	double tmp;
	if (x <= -2.35e+213) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (x <= -2.1e+99) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -6.5e+37) {
		tmp = t_2;
	} else if (x <= -6.8e-13) {
		tmp = (t * c) * (y4 * -y2);
	} else if (x <= -1e-151) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (x <= 7e-176) {
		tmp = t_1;
	} else if (x <= 1.6e-40) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (x <= 3.05e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = c * (x * ((y0 * y2) - (y * i)))
	tmp = 0
	if x <= -2.35e+213:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif x <= -2.1e+99:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -6.5e+37:
		tmp = t_2
	elif x <= -6.8e-13:
		tmp = (t * c) * (y4 * -y2)
	elif x <= -1e-151:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif x <= 7e-176:
		tmp = t_1
	elif x <= 1.6e-40:
		tmp = c * (i * ((z * t) - (x * y)))
	elif x <= 3.05e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	tmp = 0.0
	if (x <= -2.35e+213)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (x <= -2.1e+99)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -6.5e+37)
		tmp = t_2;
	elseif (x <= -6.8e-13)
		tmp = Float64(Float64(t * c) * Float64(y4 * Float64(-y2)));
	elseif (x <= -1e-151)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (x <= 7e-176)
		tmp = t_1;
	elseif (x <= 1.6e-40)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (x <= 3.05e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = c * (x * ((y0 * y2) - (y * i)));
	tmp = 0.0;
	if (x <= -2.35e+213)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (x <= -2.1e+99)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -6.5e+37)
		tmp = t_2;
	elseif (x <= -6.8e-13)
		tmp = (t * c) * (y4 * -y2);
	elseif (x <= -1e-151)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (x <= 7e-176)
		tmp = t_1;
	elseif (x <= 1.6e-40)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (x <= 3.05e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.35e+213], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e+99], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e+37], t$95$2, If[LessEqual[x, -6.8e-13], N[(N[(t * c), $MachinePrecision] * N[(y4 * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-151], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-176], t$95$1, If[LessEqual[x, 1.6e-40], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e+125], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -2.3499999999999999e213

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y2 around inf 62.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -2.3499999999999999e213 < x < -2.1000000000000001e99

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 65.8%

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

   if -2.1000000000000001e99 < x < -6.4999999999999998e37 or 3.04999999999999988e125 < x

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 58.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if -6.4999999999999998e37 < x < -6.80000000000000031e-13

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 55.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 56.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.6%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 56.6%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 56.6%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 56.6%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 57.0%

      \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(-1 \cdot \left(c \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 57.0%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(-c \cdot t\right)} \]

      2. *-commutative 57.0%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(-\color{blue}{t \cdot c}\right) \]

      3. distribute-rgt-neg-in 57.0%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(t \cdot \left(-c\right)\right)} \]

   10. Simplified 57.0%

       \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(t \cdot \left(-c\right)\right)} \]

   if -6.80000000000000031e-13 < x < -9.9999999999999994e-152

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 46.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 46.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 46.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 46.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 46.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if -9.9999999999999994e-152 < x < 7e-176 or 1.60000000000000001e-40 < x < 3.04999999999999988e125

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 7e-176 < x < 1.60000000000000001e-40

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 48.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 46.5%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+213}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(y4 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 18: 31.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ t_2 := \left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y4 \leq -7.3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;y4 \leq -1.42 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -1.75 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{+104}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* i (- (* z t) (* x y)))))
        (t_2 (* (* c y4) (- (* y y3) (* t y2)))))
   (if (<= y4 -7.3e+18)
     (* b (* y4 (- (* t j) (* y k))))
     (if (<= y4 -8.5e-45)
       (* (* y a) (- (* x b) (* y3 y5)))
       (if (<= y4 -1.42e-71)
         t_2
         (if (<= y4 -1.75e-130)
           t_1
           (if (<= y4 3.1e-305)
             (* a (* y2 (- (* t y5) (* x y1))))
             (if (<= y4 1.6e-60)
               (* c (* x (- (* y0 y2) (* y i))))
               (if (<= y4 1.55e+104)
                 (* y4 (* y1 (- (* k y2) (* j y3))))
                 (if (<= y4 1.5e+130) t_1 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * ((z * t) - (x * y)));
	double t_2 = (c * y4) * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -7.3e+18) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -8.5e-45) {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	} else if (y4 <= -1.42e-71) {
		tmp = t_2;
	} else if (y4 <= -1.75e-130) {
		tmp = t_1;
	} else if (y4 <= 3.1e-305) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y4 <= 1.6e-60) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y4 <= 1.55e+104) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y4 <= 1.5e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (i * ((z * t) - (x * y)))
    t_2 = (c * y4) * ((y * y3) - (t * y2))
    if (y4 <= (-7.3d+18)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-8.5d-45)) then
        tmp = (y * a) * ((x * b) - (y3 * y5))
    else if (y4 <= (-1.42d-71)) then
        tmp = t_2
    else if (y4 <= (-1.75d-130)) then
        tmp = t_1
    else if (y4 <= 3.1d-305) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y4 <= 1.6d-60) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y4 <= 1.55d+104) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y4 <= 1.5d+130) then
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * ((z * t) - (x * y)));
	double t_2 = (c * y4) * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -7.3e+18) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -8.5e-45) {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	} else if (y4 <= -1.42e-71) {
		tmp = t_2;
	} else if (y4 <= -1.75e-130) {
		tmp = t_1;
	} else if (y4 <= 3.1e-305) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y4 <= 1.6e-60) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y4 <= 1.55e+104) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y4 <= 1.5e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (i * ((z * t) - (x * y)))
	t_2 = (c * y4) * ((y * y3) - (t * y2))
	tmp = 0
	if y4 <= -7.3e+18:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -8.5e-45:
		tmp = (y * a) * ((x * b) - (y3 * y5))
	elif y4 <= -1.42e-71:
		tmp = t_2
	elif y4 <= -1.75e-130:
		tmp = t_1
	elif y4 <= 3.1e-305:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y4 <= 1.6e-60:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y4 <= 1.55e+104:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y4 <= 1.5e+130:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))))
	t_2 = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y4 <= -7.3e+18)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -8.5e-45)
		tmp = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)));
	elseif (y4 <= -1.42e-71)
		tmp = t_2;
	elseif (y4 <= -1.75e-130)
		tmp = t_1;
	elseif (y4 <= 3.1e-305)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y4 <= 1.6e-60)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y4 <= 1.55e+104)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y4 <= 1.5e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (i * ((z * t) - (x * y)));
	t_2 = (c * y4) * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y4 <= -7.3e+18)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -8.5e-45)
		tmp = (y * a) * ((x * b) - (y3 * y5));
	elseif (y4 <= -1.42e-71)
		tmp = t_2;
	elseif (y4 <= -1.75e-130)
		tmp = t_1;
	elseif (y4 <= 3.1e-305)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y4 <= 1.6e-60)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y4 <= 1.55e+104)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y4 <= 1.5e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -7.3e+18], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8.5e-45], N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.42e-71], t$95$2, If[LessEqual[y4, -1.75e-130], t$95$1, If[LessEqual[y4, 3.1e-305], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.6e-60], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.55e+104], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.5e+130], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y4 < -7.3e18

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 51.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 46.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 51.8%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   if -7.3e18 < y4 < -8.50000000000000041e-45

   1. Initial program 9.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 64.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 64.5%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 64.5%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. +-commutative 64.5%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      4. mul-1-neg 64.5%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      5. unsub-neg 64.5%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      6. *-commutative 64.5%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x - \color{blue}{y5 \cdot y3}\right) \]

   9. Simplified 64.5%

      \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x - y5 \cdot y3\right)} \]

   if -8.50000000000000041e-45 < y4 < -1.4199999999999999e-71 or 1.5e130 < y4

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 57.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   7. Simplified 52.9%

      \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   if -1.4199999999999999e-71 < y4 < -1.75e-130 or 1.55000000000000008e104 < y4 < 1.5e130

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 60.2%

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

   if -1.75e-130 < y4 < 3.0999999999999998e-305

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 41.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 41.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 41.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 45.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if 3.0999999999999998e-305 < y4 < 1.6000000000000001e-60

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 56.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 56.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 47.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if 1.6000000000000001e-60 < y4 < 1.55000000000000008e104

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 45.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 45.7%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 45.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -7.3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-45}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;y4 \leq -1.42 \cdot 10^{-71}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;y4 \leq -1.75 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{+104}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{+130}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \end{array} \]

Alternative 19: 31.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (* i (- (* t c) (* k y1))))))
   (if (<= a -1.05e+160)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= a -3.8e+19)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= a -3e-51)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= a -2.55e-66)
           t_1
           (if (<= a -1e-277)
             (* z (* k (- (* b y0) (* i y1))))
             (if (<= a 1.22e-171)
               (* c (* x (- (* y0 y2) (* y i))))
               (if (<= a 8.5e-56)
                 t_1
                 (if (<= a 9.5e+146)
                   (* a (* y2 (- (* t y5) (* x y1))))
                   (* (* y a) (- (* x b) (* y3 y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (i * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -1.05e+160) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -3.8e+19) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (a <= -3e-51) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -2.55e-66) {
		tmp = t_1;
	} else if (a <= -1e-277) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else if (a <= 1.22e-171) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 8.5e-56) {
		tmp = t_1;
	} else if (a <= 9.5e+146) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (i * ((t * c) - (k * y1)))
    if (a <= (-1.05d+160)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (a <= (-3.8d+19)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (a <= (-3d-51)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-2.55d-66)) then
        tmp = t_1
    else if (a <= (-1d-277)) then
        tmp = z * (k * ((b * y0) - (i * y1)))
    else if (a <= 1.22d-171) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (a <= 8.5d-56) then
        tmp = t_1
    else if (a <= 9.5d+146) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else
        tmp = (y * a) * ((x * b) - (y3 * y5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (i * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -1.05e+160) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (a <= -3.8e+19) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (a <= -3e-51) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -2.55e-66) {
		tmp = t_1;
	} else if (a <= -1e-277) {
		tmp = z * (k * ((b * y0) - (i * y1)));
	} else if (a <= 1.22e-171) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (a <= 8.5e-56) {
		tmp = t_1;
	} else if (a <= 9.5e+146) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = (y * a) * ((x * b) - (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * (i * ((t * c) - (k * y1)))
	tmp = 0
	if a <= -1.05e+160:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif a <= -3.8e+19:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif a <= -3e-51:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -2.55e-66:
		tmp = t_1
	elif a <= -1e-277:
		tmp = z * (k * ((b * y0) - (i * y1)))
	elif a <= 1.22e-171:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif a <= 8.5e-56:
		tmp = t_1
	elif a <= 9.5e+146:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	else:
		tmp = (y * a) * ((x * b) - (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(i * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (a <= -1.05e+160)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (a <= -3.8e+19)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (a <= -3e-51)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -2.55e-66)
		tmp = t_1;
	elseif (a <= -1e-277)
		tmp = Float64(z * Float64(k * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (a <= 1.22e-171)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (a <= 8.5e-56)
		tmp = t_1;
	elseif (a <= 9.5e+146)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	else
		tmp = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * (i * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (a <= -1.05e+160)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (a <= -3.8e+19)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (a <= -3e-51)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -2.55e-66)
		tmp = t_1;
	elseif (a <= -1e-277)
		tmp = z * (k * ((b * y0) - (i * y1)));
	elseif (a <= 1.22e-171)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (a <= 8.5e-56)
		tmp = t_1;
	elseif (a <= 9.5e+146)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	else
		tmp = (y * a) * ((x * b) - (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(i * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+160], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e+19], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-51], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-66], t$95$1, If[LessEqual[a, -1e-277], N[(z * N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-171], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-56], t$95$1, If[LessEqual[a, 9.5e+146], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.04999999999999998e160

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y5 around inf 66.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot \left(y5 \cdot y2\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 69.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y5\right) \cdot y2} \]

      2. *-commutative 69.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right)\right)} \cdot y2 \]

      3. associate-*l* 66.0%

         \[\leadsto \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) - -1 \cdot \left(a \cdot t\right)\right) \cdot y2\right)} \]

      4. cancel-sign-sub-inv 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(-1 \cdot \left(k \cdot y0\right) + \left(--1\right) \cdot \left(a \cdot t\right)\right)} \cdot y2\right) \]

      5. metadata-eval 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{1} \cdot \left(a \cdot t\right)\right) \cdot y2\right) \]

      6. *-lft-identity 66.0%

         \[\leadsto y5 \cdot \left(\left(-1 \cdot \left(k \cdot y0\right) + \color{blue}{a \cdot t}\right) \cdot y2\right) \]

      7. +-commutative 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t + -1 \cdot \left(k \cdot y0\right)\right)} \cdot y2\right) \]

      8. mul-1-neg 66.0%

         \[\leadsto y5 \cdot \left(\left(a \cdot t + \color{blue}{\left(-k \cdot y0\right)}\right) \cdot y2\right) \]

      9. unsub-neg 66.0%

         \[\leadsto y5 \cdot \left(\color{blue}{\left(a \cdot t - k \cdot y0\right)} \cdot y2\right) \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{y5 \cdot \left(\left(a \cdot t - k \cdot y0\right) \cdot y2\right)} \]

   if -1.04999999999999998e160 < a < -3.8e19

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 58.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 58.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.7%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   7. Simplified 52.7%

      \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

   if -3.8e19 < a < -3.00000000000000002e-51

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 26.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 53.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   if -3.00000000000000002e-51 < a < -2.55000000000000011e-66 or 1.2199999999999999e-171 < a < 8.49999999999999932e-56

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 36.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in i around inf 51.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot \left(i \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\left(-1 \cdot \left(c \cdot t\right) - -1 \cdot \left(k \cdot y1\right)\right) \cdot i\right) \cdot z\right)} \]

      2. distribute-lft-out-- 57.9%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(-1 \cdot \left(c \cdot t - k \cdot y1\right)\right)} \cdot i\right) \cdot z\right) \]

      3. associate-*r* 57.9%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-1 \cdot \left(\left(c \cdot t - k \cdot y1\right) \cdot i\right)\right)} \cdot z\right) \]

      4. mul-1-neg 57.9%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(-\left(c \cdot t - k \cdot y1\right) \cdot i\right)} \cdot z\right) \]

      5. *-commutative 57.9%

         \[\leadsto -1 \cdot \left(\left(-\color{blue}{i \cdot \left(c \cdot t - k \cdot y1\right)}\right) \cdot z\right) \]

      6. *-commutative 57.9%

         \[\leadsto -1 \cdot \left(\left(-i \cdot \left(\color{blue}{t \cdot c} - k \cdot y1\right)\right) \cdot z\right) \]

   7. Simplified 57.9%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(-i \cdot \left(t \cdot c - k \cdot y1\right)\right) \cdot z\right)} \]

   if -2.55000000000000011e-66 < a < -9.99999999999999969e-278

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 39.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 40.1%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   if -9.99999999999999969e-278 < a < 1.2199999999999999e-171

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in x around inf 49.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2 - y \cdot i\right) \cdot x\right)} \]

   if 8.49999999999999932e-56 < a < 9.49999999999999926e146

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if 9.49999999999999926e146 < a

   1. Initial program 9.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 9.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 9.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 52.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 52.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 52.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 52.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 67.1%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. +-commutative 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      4. mul-1-neg 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      5. unsub-neg 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      6. *-commutative 67.1%

         \[\leadsto \left(y \cdot a\right) \cdot \left(b \cdot x - \color{blue}{y5 \cdot y3}\right) \]

   9. Simplified 67.1%

      \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x - y5 \cdot y3\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+19}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(i \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \end{array} \]

Alternative 20: 27.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-253}:\\ \;\;\;\;\left(k \cdot \left(i \cdot y1\right)\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y2 (- (* t y5) (* x y1)))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= x -3.4e-16)
     (* a (* b (- (* x y) (* z t))))
     (if (<= x -9.5e-154)
       t_1
       (if (<= x 9.5e-253)
         (* (* k (* i y1)) (- z))
         (if (<= x 1.75e-179)
           t_2
           (if (<= x 3.5e-119)
             (* b (* (- k) (* y y4)))
             (if (<= x 1.42e+107) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * ((t * y5) - (x * y1)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (x <= -3.4e-16) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -9.5e-154) {
		tmp = t_1;
	} else if (x <= 9.5e-253) {
		tmp = (k * (i * y1)) * -z;
	} else if (x <= 1.75e-179) {
		tmp = t_2;
	} else if (x <= 3.5e-119) {
		tmp = b * (-k * (y * y4));
	} else if (x <= 1.42e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y2 * ((t * y5) - (x * y1)))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (x <= (-3.4d-16)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (x <= (-9.5d-154)) then
        tmp = t_1
    else if (x <= 9.5d-253) then
        tmp = (k * (i * y1)) * -z
    else if (x <= 1.75d-179) then
        tmp = t_2
    else if (x <= 3.5d-119) then
        tmp = b * (-k * (y * y4))
    else if (x <= 1.42d+107) then
        tmp = t_2
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y2 * ((t * y5) - (x * y1)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (x <= -3.4e-16) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (x <= -9.5e-154) {
		tmp = t_1;
	} else if (x <= 9.5e-253) {
		tmp = (k * (i * y1)) * -z;
	} else if (x <= 1.75e-179) {
		tmp = t_2;
	} else if (x <= 3.5e-119) {
		tmp = b * (-k * (y * y4));
	} else if (x <= 1.42e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y2 * ((t * y5) - (x * y1)))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if x <= -3.4e-16:
		tmp = a * (b * ((x * y) - (z * t)))
	elif x <= -9.5e-154:
		tmp = t_1
	elif x <= 9.5e-253:
		tmp = (k * (i * y1)) * -z
	elif x <= 1.75e-179:
		tmp = t_2
	elif x <= 3.5e-119:
		tmp = b * (-k * (y * y4))
	elif x <= 1.42e+107:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (x <= -3.4e-16)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (x <= -9.5e-154)
		tmp = t_1;
	elseif (x <= 9.5e-253)
		tmp = Float64(Float64(k * Float64(i * y1)) * Float64(-z));
	elseif (x <= 1.75e-179)
		tmp = t_2;
	elseif (x <= 3.5e-119)
		tmp = Float64(b * Float64(Float64(-k) * Float64(y * y4)));
	elseif (x <= 1.42e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y2 * ((t * y5) - (x * y1)));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (x <= -3.4e-16)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (x <= -9.5e-154)
		tmp = t_1;
	elseif (x <= 9.5e-253)
		tmp = (k * (i * y1)) * -z;
	elseif (x <= 1.75e-179)
		tmp = t_2;
	elseif (x <= 3.5e-119)
		tmp = b * (-k * (y * y4));
	elseif (x <= 1.42e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-16], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-154], t$95$1, If[LessEqual[x, 9.5e-253], N[(N[(k * N[(i * y1), $MachinePrecision]), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[x, 1.75e-179], t$95$2, If[LessEqual[x, 3.5e-119], N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.42e+107], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.4e-16

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 41.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 41.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 41.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.2%

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

   if -3.4e-16 < x < -9.50000000000000057e-154 or 1.42000000000000006e107 < x

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 33.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 33.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 33.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 33.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 48.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if -9.50000000000000057e-154 < x < 9.5e-253

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 44.3%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 34.2%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right)} \cdot z\right) \]

   if 9.5e-253 < x < 1.75000000000000012e-179 or 3.5e-119 < x < 1.42000000000000006e107

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 37.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 37.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 37.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 37.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if 1.75000000000000012e-179 < x < 3.5e-119

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 54.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 41.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 47.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 47.5%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 47.5%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 47.5%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-253}:\\ \;\;\;\;\left(k \cdot \left(i \cdot y1\right)\right) \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \]

Alternative 21: 30.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-252}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i))))))
   (if (<= c -3.4e+52)
     t_1
     (if (<= c -4.5e-147)
       (* a (* b (- (* x y) (* z t))))
       (if (<= c -2.3e-216)
         (* a (* y2 (- (* t y5) (* x y1))))
         (if (<= c -2.6e-252)
           (* y4 (* t (* b j)))
           (if (<= c 5.4e-201)
             (* b (* (- k) (* y y4)))
             (if (<= c 1.8e+73) (* a (* y5 (- (* t y2) (* y y3)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double tmp;
	if (c <= -3.4e+52) {
		tmp = t_1;
	} else if (c <= -4.5e-147) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (c <= -2.3e-216) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (c <= -2.6e-252) {
		tmp = y4 * (t * (b * j));
	} else if (c <= 5.4e-201) {
		tmp = b * (-k * (y * y4));
	} else if (c <= 1.8e+73) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y * ((y3 * y4) - (x * i)))
    if (c <= (-3.4d+52)) then
        tmp = t_1
    else if (c <= (-4.5d-147)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (c <= (-2.3d-216)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (c <= (-2.6d-252)) then
        tmp = y4 * (t * (b * j))
    else if (c <= 5.4d-201) then
        tmp = b * (-k * (y * y4))
    else if (c <= 1.8d+73) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double tmp;
	if (c <= -3.4e+52) {
		tmp = t_1;
	} else if (c <= -4.5e-147) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (c <= -2.3e-216) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (c <= -2.6e-252) {
		tmp = y4 * (t * (b * j));
	} else if (c <= 5.4e-201) {
		tmp = b * (-k * (y * y4));
	} else if (c <= 1.8e+73) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y * ((y3 * y4) - (x * i)))
	tmp = 0
	if c <= -3.4e+52:
		tmp = t_1
	elif c <= -4.5e-147:
		tmp = a * (b * ((x * y) - (z * t)))
	elif c <= -2.3e-216:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif c <= -2.6e-252:
		tmp = y4 * (t * (b * j))
	elif c <= 5.4e-201:
		tmp = b * (-k * (y * y4))
	elif c <= 1.8e+73:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	tmp = 0.0
	if (c <= -3.4e+52)
		tmp = t_1;
	elseif (c <= -4.5e-147)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (c <= -2.3e-216)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (c <= -2.6e-252)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (c <= 5.4e-201)
		tmp = Float64(b * Float64(Float64(-k) * Float64(y * y4)));
	elseif (c <= 1.8e+73)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * ((y3 * y4) - (x * i)));
	tmp = 0.0;
	if (c <= -3.4e+52)
		tmp = t_1;
	elseif (c <= -4.5e-147)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (c <= -2.3e-216)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (c <= -2.6e-252)
		tmp = y4 * (t * (b * j));
	elseif (c <= 5.4e-201)
		tmp = b * (-k * (y * y4));
	elseif (c <= 1.8e+73)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.4e+52], t$95$1, If[LessEqual[c, -4.5e-147], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-216], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-252], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-201], N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+73], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -3.4e52 or 1.7999999999999999e73 < c

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 59.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 59.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in y around -inf 48.8%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 48.8%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 48.8%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 48.8%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

   9. Simplified 48.8%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - i \cdot x\right)\right)} \]

   if -3.4e52 < c < -4.49999999999999973e-147

   1. Initial program 18.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 48.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 48.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 48.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 48.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 48.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 46.9%

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

   if -4.49999999999999973e-147 < c < -2.29999999999999997e-216

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 43.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 43.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 43.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]

   if -2.29999999999999997e-216 < c < -2.5999999999999999e-252

   1. Initial program 49.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 49.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 49.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 50.6%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if -2.5999999999999999e-252 < c < 5.40000000000000011e-201

   1. Initial program 18.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 39.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.1%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 44.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 44.6%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 44.6%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 44.6%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   if 5.40000000000000011e-201 < c < 1.7999999999999999e73

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 39.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-252}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \]

Alternative 22: 22.5% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ t_2 := y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{if}\;y3 \leq -8.5 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{-297}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* x y)))) (t_2 (* y4 (* y1 (* j (- y3))))))
   (if (<= y3 -8.5e+57)
     t_2
     (if (<= y3 -6.5e-54)
       (* a (* b (* z (- t))))
       (if (<= y3 2.3e-297)
         (* y4 (* k (* y1 y2)))
         (if (<= y3 7.8e-194)
           t_1
           (if (<= y3 9.2e+79)
             (* a (* z (* t (- b))))
             (if (<= y3 3.2e+164) t_1 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double t_2 = y4 * (y1 * (j * -y3));
	double tmp;
	if (y3 <= -8.5e+57) {
		tmp = t_2;
	} else if (y3 <= -6.5e-54) {
		tmp = a * (b * (z * -t));
	} else if (y3 <= 2.3e-297) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y3 <= 7.8e-194) {
		tmp = t_1;
	} else if (y3 <= 9.2e+79) {
		tmp = a * (z * (t * -b));
	} else if (y3 <= 3.2e+164) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * (x * y))
    t_2 = y4 * (y1 * (j * -y3))
    if (y3 <= (-8.5d+57)) then
        tmp = t_2
    else if (y3 <= (-6.5d-54)) then
        tmp = a * (b * (z * -t))
    else if (y3 <= 2.3d-297) then
        tmp = y4 * (k * (y1 * y2))
    else if (y3 <= 7.8d-194) then
        tmp = t_1
    else if (y3 <= 9.2d+79) then
        tmp = a * (z * (t * -b))
    else if (y3 <= 3.2d+164) then
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double t_2 = y4 * (y1 * (j * -y3));
	double tmp;
	if (y3 <= -8.5e+57) {
		tmp = t_2;
	} else if (y3 <= -6.5e-54) {
		tmp = a * (b * (z * -t));
	} else if (y3 <= 2.3e-297) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y3 <= 7.8e-194) {
		tmp = t_1;
	} else if (y3 <= 9.2e+79) {
		tmp = a * (z * (t * -b));
	} else if (y3 <= 3.2e+164) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * (x * y))
	t_2 = y4 * (y1 * (j * -y3))
	tmp = 0
	if y3 <= -8.5e+57:
		tmp = t_2
	elif y3 <= -6.5e-54:
		tmp = a * (b * (z * -t))
	elif y3 <= 2.3e-297:
		tmp = y4 * (k * (y1 * y2))
	elif y3 <= 7.8e-194:
		tmp = t_1
	elif y3 <= 9.2e+79:
		tmp = a * (z * (t * -b))
	elif y3 <= 3.2e+164:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(x * y)))
	t_2 = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))))
	tmp = 0.0
	if (y3 <= -8.5e+57)
		tmp = t_2;
	elseif (y3 <= -6.5e-54)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (y3 <= 2.3e-297)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (y3 <= 7.8e-194)
		tmp = t_1;
	elseif (y3 <= 9.2e+79)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (y3 <= 3.2e+164)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * (x * y));
	t_2 = y4 * (y1 * (j * -y3));
	tmp = 0.0;
	if (y3 <= -8.5e+57)
		tmp = t_2;
	elseif (y3 <= -6.5e-54)
		tmp = a * (b * (z * -t));
	elseif (y3 <= 2.3e-297)
		tmp = y4 * (k * (y1 * y2));
	elseif (y3 <= 7.8e-194)
		tmp = t_1;
	elseif (y3 <= 9.2e+79)
		tmp = a * (z * (t * -b));
	elseif (y3 <= 3.2e+164)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -8.5e+57], t$95$2, If[LessEqual[y3, -6.5e-54], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.3e-297], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.8e-194], t$95$1, If[LessEqual[y3, 9.2e+79], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.2e+164], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -8.5000000000000001e57 or 3.1999999999999998e164 < y3

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 39.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 39.7%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 39.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 37.4%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 37.4%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 37.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 37.4%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   if -8.5000000000000001e57 < y3 < -6.49999999999999991e-54

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 37.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 37.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 37.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 37.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 37.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.6%

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

   8. Taylor expanded in y around 0 38.4%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 38.4%

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

      2. distribute-lft-neg-in 38.4%

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

      3. *-commutative 38.4%

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

   10. Simplified 38.4%

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

   if -6.49999999999999991e-54 < y3 < 2.2999999999999999e-297

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 22.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 22.6%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 22.6%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 22.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 28.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 28.0%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if 2.2999999999999999e-297 < y3 < 7.7999999999999997e-194 or 9.2000000000000002e79 < y3 < 3.1999999999999998e164

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 34.0%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 34.0%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 34.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 34.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 34.1%

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

   8. Taylor expanded in y around inf 34.5%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 7.7999999999999997e-194 < y3 < 9.2000000000000002e79

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 37.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 37.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 37.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 37.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 37.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.3%

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

   8. Taylor expanded in y around 0 23.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 23.5%

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

      2. *-commutative 23.5%

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

      3. associate-*r* 25.2%

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

      4. distribute-rgt-neg-in 25.2%

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

   10. Simplified 25.2%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -8.5 \cdot 10^{+57}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.3 \cdot 10^{-297}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq 9.2 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 23: 19.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{if}\;k \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;\left(-b\right) \cdot \left(\left(y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-137}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.15 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+241}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (* x y)))))
   (if (<= k -5.8e+29)
     (* (- b) (* (* y k) y4))
     (if (<= k 4.4e-268)
       t_1
       (if (<= k 1.7e-137)
         (* k (* y4 (* y1 y2)))
         (if (<= k 1.22e+59)
           (* a (* b (* z (- t))))
           (if (<= k 3.15e+190)
             (* y4 (* y2 (* k y1)))
             (if (<= k 1.22e+241) (* y4 (* y1 (* j (- y3)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (k <= -5.8e+29) {
		tmp = -b * ((y * k) * y4);
	} else if (k <= 4.4e-268) {
		tmp = t_1;
	} else if (k <= 1.7e-137) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= 1.22e+59) {
		tmp = a * (b * (z * -t));
	} else if (k <= 3.15e+190) {
		tmp = y4 * (y2 * (k * y1));
	} else if (k <= 1.22e+241) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (x * y))
    if (k <= (-5.8d+29)) then
        tmp = -b * ((y * k) * y4)
    else if (k <= 4.4d-268) then
        tmp = t_1
    else if (k <= 1.7d-137) then
        tmp = k * (y4 * (y1 * y2))
    else if (k <= 1.22d+59) then
        tmp = a * (b * (z * -t))
    else if (k <= 3.15d+190) then
        tmp = y4 * (y2 * (k * y1))
    else if (k <= 1.22d+241) then
        tmp = y4 * (y1 * (j * -y3))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * (x * y));
	double tmp;
	if (k <= -5.8e+29) {
		tmp = -b * ((y * k) * y4);
	} else if (k <= 4.4e-268) {
		tmp = t_1;
	} else if (k <= 1.7e-137) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= 1.22e+59) {
		tmp = a * (b * (z * -t));
	} else if (k <= 3.15e+190) {
		tmp = y4 * (y2 * (k * y1));
	} else if (k <= 1.22e+241) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * (x * y))
	tmp = 0
	if k <= -5.8e+29:
		tmp = -b * ((y * k) * y4)
	elif k <= 4.4e-268:
		tmp = t_1
	elif k <= 1.7e-137:
		tmp = k * (y4 * (y1 * y2))
	elif k <= 1.22e+59:
		tmp = a * (b * (z * -t))
	elif k <= 3.15e+190:
		tmp = y4 * (y2 * (k * y1))
	elif k <= 1.22e+241:
		tmp = y4 * (y1 * (j * -y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(x * y)))
	tmp = 0.0
	if (k <= -5.8e+29)
		tmp = Float64(Float64(-b) * Float64(Float64(y * k) * y4));
	elseif (k <= 4.4e-268)
		tmp = t_1;
	elseif (k <= 1.7e-137)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (k <= 1.22e+59)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (k <= 3.15e+190)
		tmp = Float64(y4 * Float64(y2 * Float64(k * y1)));
	elseif (k <= 1.22e+241)
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * (x * y));
	tmp = 0.0;
	if (k <= -5.8e+29)
		tmp = -b * ((y * k) * y4);
	elseif (k <= 4.4e-268)
		tmp = t_1;
	elseif (k <= 1.7e-137)
		tmp = k * (y4 * (y1 * y2));
	elseif (k <= 1.22e+59)
		tmp = a * (b * (z * -t));
	elseif (k <= 3.15e+190)
		tmp = y4 * (y2 * (k * y1));
	elseif (k <= 1.22e+241)
		tmp = y4 * (y1 * (j * -y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.8e+29], N[((-b) * N[(N[(y * k), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.4e-268], t$95$1, If[LessEqual[k, 1.7e-137], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e+59], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.15e+190], N[(y4 * N[(y2 * N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e+241], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -5.7999999999999999e29

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 49.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 51.8%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 45.9%

      \[\leadsto \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y\right)\right)}\right) \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 45.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(-k \cdot y\right)}\right) \cdot b \]

      2. distribute-lft-neg-out 45.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(\left(-k\right) \cdot y\right)}\right) \cdot b \]

      3. *-commutative 45.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \cdot b \]

   10. Simplified 45.9%

       \[\leadsto \left(y4 \cdot \color{blue}{\left(y \cdot \left(-k\right)\right)}\right) \cdot b \]

   if -5.7999999999999999e29 < k < 4.40000000000000008e-268 or 1.22e241 < k

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 38.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 38.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 38.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 38.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.7%

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

   8. Taylor expanded in y around inf 23.4%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 4.40000000000000008e-268 < k < 1.70000000000000007e-137

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 39.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 27.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 23.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 23.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 23.7%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 23.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 32.2%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.2%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 32.2%

       \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1\right)\right)} \]

   if 1.70000000000000007e-137 < k < 1.22e59

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 38.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 27.3%

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

   8. Taylor expanded in y around 0 33.6%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 33.6%

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

      2. distribute-lft-neg-in 33.6%

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

      3. *-commutative 33.6%

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

   10. Simplified 33.6%

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

   if 1.22e59 < k < 3.1500000000000001e190

   1. Initial program 18.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.0%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 37.0%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 34.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto k \cdot \color{blue}{\left(\left(y1 \cdot y2\right) \cdot y4\right)} \]

      2. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right) \cdot y4} \]

      3. associate-*r* 43.4%

         \[\leadsto \color{blue}{\left(\left(k \cdot y1\right) \cdot y2\right)} \cdot y4 \]

      4. *-commutative 43.4%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(k \cdot y1\right)\right)} \cdot y4 \]

      5. *-commutative 43.4%

         \[\leadsto \left(y2 \cdot \color{blue}{\left(y1 \cdot k\right)}\right) \cdot y4 \]

   10. Simplified 43.4%

       \[\leadsto \color{blue}{\left(y2 \cdot \left(y1 \cdot k\right)\right) \cdot y4} \]

   if 3.1500000000000001e190 < k < 1.22e241

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 44.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 44.6%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 44.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 56.3%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 56.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 56.3%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 56.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 56.3%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;\left(-b\right) \cdot \left(\left(y \cdot k\right) \cdot y4\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{-137}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.15 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{+241}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 24: 27.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-220}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (- k) (* y y4))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y4 -2.05e-10)
     t_1
     (if (<= y4 -2.7e-164)
       t_2
       (if (<= y4 -8.5e-220)
         (* k (- (* i (* z y1))))
         (if (<= y4 1.4e+35) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y4 <= -2.05e-10) {
		tmp = t_1;
	} else if (y4 <= -2.7e-164) {
		tmp = t_2;
	} else if (y4 <= -8.5e-220) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 1.4e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (-k * (y * y4))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (y4 <= (-2.05d-10)) then
        tmp = t_1
    else if (y4 <= (-2.7d-164)) then
        tmp = t_2
    else if (y4 <= (-8.5d-220)) then
        tmp = k * -(i * (z * y1))
    else if (y4 <= 1.4d+35) then
        tmp = t_2
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y4 <= -2.05e-10) {
		tmp = t_1;
	} else if (y4 <= -2.7e-164) {
		tmp = t_2;
	} else if (y4 <= -8.5e-220) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 1.4e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (-k * (y * y4))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y4 <= -2.05e-10:
		tmp = t_1
	elif y4 <= -2.7e-164:
		tmp = t_2
	elif y4 <= -8.5e-220:
		tmp = k * -(i * (z * y1))
	elif y4 <= 1.4e+35:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(-k) * Float64(y * y4)))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y4 <= -2.05e-10)
		tmp = t_1;
	elseif (y4 <= -2.7e-164)
		tmp = t_2;
	elseif (y4 <= -8.5e-220)
		tmp = Float64(k * Float64(-Float64(i * Float64(z * y1))));
	elseif (y4 <= 1.4e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (-k * (y * y4));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y4 <= -2.05e-10)
		tmp = t_1;
	elseif (y4 <= -2.7e-164)
		tmp = t_2;
	elseif (y4 <= -8.5e-220)
		tmp = k * -(i * (z * y1));
	elseif (y4 <= 1.4e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.05e-10], t$95$1, If[LessEqual[y4, -2.7e-164], t$95$2, If[LessEqual[y4, -8.5e-220], N[(k * (-N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y4, 1.4e+35], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -2.0499999999999999e-10 or 1.39999999999999999e35 < y4

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 44.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 43.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 43.7%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 43.7%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   if -2.0499999999999999e-10 < y4 < -2.7000000000000001e-164 or -8.4999999999999996e-220 < y4 < 1.39999999999999999e35

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 41.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 41.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 41.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -2.7000000000000001e-164 < y4 < -8.4999999999999996e-220

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 38.0%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 20.4%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 20.4%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot z\right) \cdot y1\right)}\right) \]

      2. associate-*r* 46.7%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(z \cdot y1\right)\right)}\right) \]

   8. Simplified 46.7%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-220}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 25: 30.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -7 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-283}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -7e+35)
     t_1
     (if (<= y5 2.05e-283)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y5 3.9e-38)
         (* t (* j (* b y4)))
         (if (<= y5 1.95e+99) (* a (* y2 (- (* t y5) (* x y1)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -7e+35) {
		tmp = t_1;
	} else if (y5 <= 2.05e-283) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y5 <= 3.9e-38) {
		tmp = t * (j * (b * y4));
	} else if (y5 <= 1.95e+99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (y5 <= (-7d+35)) then
        tmp = t_1
    else if (y5 <= 2.05d-283) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y5 <= 3.9d-38) then
        tmp = t * (j * (b * y4))
    else if (y5 <= 1.95d+99) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -7e+35) {
		tmp = t_1;
	} else if (y5 <= 2.05e-283) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y5 <= 3.9e-38) {
		tmp = t * (j * (b * y4));
	} else if (y5 <= 1.95e+99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y5 <= -7e+35:
		tmp = t_1
	elif y5 <= 2.05e-283:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y5 <= 3.9e-38:
		tmp = t * (j * (b * y4))
	elif y5 <= 1.95e+99:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -7e+35)
		tmp = t_1;
	elseif (y5 <= 2.05e-283)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y5 <= 3.9e-38)
		tmp = Float64(t * Float64(j * Float64(b * y4)));
	elseif (y5 <= 1.95e+99)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y5 <= -7e+35)
		tmp = t_1;
	elseif (y5 <= 2.05e-283)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y5 <= 3.9e-38)
		tmp = t * (j * (b * y4));
	elseif (y5 <= 1.95e+99)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -7e+35], t$95$1, If[LessEqual[y5, 2.05e-283], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.9e-38], N[(t * N[(j * N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.95e+99], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -7.0000000000000001e35 or 1.94999999999999997e99 < y5

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 38.7%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y5 around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)} \]

   if -7.0000000000000001e35 < y5 < 2.04999999999999993e-283

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 51.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   7. Taylor expanded in i around inf 37.1%

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

   if 2.04999999999999993e-283 < y5 < 3.8999999999999999e-38

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 40.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 40.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 38.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 38.8%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 32.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(j \cdot b\right) \cdot t\right)} \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(j \cdot b\right)\right) \cdot t} \]

      3. *-commutative 35.8%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(b \cdot j\right)}\right) \cdot t \]

      4. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot b\right) \cdot j\right)} \cdot t \]

      5. *-commutative 35.7%

         \[\leadsto \left(\color{blue}{\left(b \cdot y4\right)} \cdot j\right) \cdot t \]

      6. *-commutative 35.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(b \cdot y4\right)\right)} \cdot t \]

      7. *-commutative 35.7%

         \[\leadsto \left(j \cdot \color{blue}{\left(y4 \cdot b\right)}\right) \cdot t \]

   10. Simplified 35.7%

       \[\leadsto \color{blue}{\left(j \cdot \left(y4 \cdot b\right)\right) \cdot t} \]

   if 3.8999999999999999e-38 < y5 < 1.94999999999999997e99

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 48.4%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 48.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 48.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 48.4%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 48.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 61.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -7 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{-283}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]

Alternative 26: 21.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+110}:\\ \;\;\;\;k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-295}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.9 \cdot 10^{-11}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.2e+110)
   (* k (- (* y4 (* y b))))
   (if (<= y4 -8e-125)
     (* z (* k (* b y0)))
     (if (<= y4 -1.5e-295)
       (* k (- (* i (* z y1))))
       (if (<= y4 3.6e-121)
         (* a (* b (* z (- t))))
         (if (<= y4 4.9e-11)
           (* y4 (* y1 (* j (- y3))))
           (* b (* (- k) (* y y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.2e+110) {
		tmp = k * -(y4 * (y * b));
	} else if (y4 <= -8e-125) {
		tmp = z * (k * (b * y0));
	} else if (y4 <= -1.5e-295) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 3.6e-121) {
		tmp = a * (b * (z * -t));
	} else if (y4 <= 4.9e-11) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = b * (-k * (y * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.2d+110)) then
        tmp = k * -(y4 * (y * b))
    else if (y4 <= (-8d-125)) then
        tmp = z * (k * (b * y0))
    else if (y4 <= (-1.5d-295)) then
        tmp = k * -(i * (z * y1))
    else if (y4 <= 3.6d-121) then
        tmp = a * (b * (z * -t))
    else if (y4 <= 4.9d-11) then
        tmp = y4 * (y1 * (j * -y3))
    else
        tmp = b * (-k * (y * y4))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.2e+110) {
		tmp = k * -(y4 * (y * b));
	} else if (y4 <= -8e-125) {
		tmp = z * (k * (b * y0));
	} else if (y4 <= -1.5e-295) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 3.6e-121) {
		tmp = a * (b * (z * -t));
	} else if (y4 <= 4.9e-11) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = b * (-k * (y * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.2e+110:
		tmp = k * -(y4 * (y * b))
	elif y4 <= -8e-125:
		tmp = z * (k * (b * y0))
	elif y4 <= -1.5e-295:
		tmp = k * -(i * (z * y1))
	elif y4 <= 3.6e-121:
		tmp = a * (b * (z * -t))
	elif y4 <= 4.9e-11:
		tmp = y4 * (y1 * (j * -y3))
	else:
		tmp = b * (-k * (y * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.2e+110)
		tmp = Float64(k * Float64(-Float64(y4 * Float64(y * b))));
	elseif (y4 <= -8e-125)
		tmp = Float64(z * Float64(k * Float64(b * y0)));
	elseif (y4 <= -1.5e-295)
		tmp = Float64(k * Float64(-Float64(i * Float64(z * y1))));
	elseif (y4 <= 3.6e-121)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (y4 <= 4.9e-11)
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	else
		tmp = Float64(b * Float64(Float64(-k) * Float64(y * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.2e+110)
		tmp = k * -(y4 * (y * b));
	elseif (y4 <= -8e-125)
		tmp = z * (k * (b * y0));
	elseif (y4 <= -1.5e-295)
		tmp = k * -(i * (z * y1));
	elseif (y4 <= 3.6e-121)
		tmp = a * (b * (z * -t));
	elseif (y4 <= 4.9e-11)
		tmp = y4 * (y1 * (j * -y3));
	else
		tmp = b * (-k * (y * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.2e+110], N[(k * (-N[(y4 * N[(y * b), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y4, -8e-125], N[(z * N[(k * N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.5e-295], N[(k * (-N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y4, 3.6e-121], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.9e-11], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.20000000000000006e110

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 16.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 67.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.3%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 56.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)\right)} \]

   if -1.20000000000000006e110 < y4 < -8.0000000000000001e-125

   1. Initial program 18.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 39.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 37.5%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around 0 31.6%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(-1 \cdot \left(k \cdot \left(y0 \cdot b\right)\right)\right)} \cdot z\right) \]
   7. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y0 \cdot b\right)\right)} \cdot z\right) \]

      2. neg-mul-1 31.6%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{\left(-k\right)} \cdot \left(y0 \cdot b\right)\right) \cdot z\right) \]

      3. *-commutative 31.6%

         \[\leadsto -1 \cdot \left(\left(\left(-k\right) \cdot \color{blue}{\left(b \cdot y0\right)}\right) \cdot z\right) \]

   8. Simplified 31.6%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(-k\right) \cdot \left(b \cdot y0\right)\right)} \cdot z\right) \]

   if -8.0000000000000001e-125 < y4 < -1.49999999999999998e-295

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 28.9%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 24.0%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 24.0%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot z\right) \cdot y1\right)}\right) \]

      2. associate-*r* 31.2%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(z \cdot y1\right)\right)}\right) \]

   8. Simplified 31.2%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right)\right)} \]

   if -1.49999999999999998e-295 < y4 < 3.59999999999999984e-121

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 31.4%

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

   8. Taylor expanded in y around 0 24.0%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 24.0%

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

      2. distribute-lft-neg-in 24.0%

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

      3. *-commutative 24.0%

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

   10. Simplified 24.0%

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

   if 3.59999999999999984e-121 < y4 < 4.8999999999999999e-11

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 30.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 30.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 30.2%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 30.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 29.7%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 29.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 29.7%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 29.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 29.7%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   if 4.8999999999999999e-11 < y4

   1. Initial program 14.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 41.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.1%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 44.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 45.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 45.5%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 45.5%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 45.5%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+110}:\\ \;\;\;\;k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-295}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.9 \cdot 10^{-11}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 27: 21.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* t (* b j)))))
   (if (<= j -2.1e+15)
     t_1
     (if (<= j -1.05e-257)
       (* a (* z (* t (- b))))
       (if (<= j 3.1e-220)
         (* a (* y (* x b)))
         (if (<= j 3.3e+17)
           (* a (* b (* z (- t))))
           (if (<= j 1.1e+129) (* (* k y2) (* y1 y4)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (j <= -2.1e+15) {
		tmp = t_1;
	} else if (j <= -1.05e-257) {
		tmp = a * (z * (t * -b));
	} else if (j <= 3.1e-220) {
		tmp = a * (y * (x * b));
	} else if (j <= 3.3e+17) {
		tmp = a * (b * (z * -t));
	} else if (j <= 1.1e+129) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (t * (b * j))
    if (j <= (-2.1d+15)) then
        tmp = t_1
    else if (j <= (-1.05d-257)) then
        tmp = a * (z * (t * -b))
    else if (j <= 3.1d-220) then
        tmp = a * (y * (x * b))
    else if (j <= 3.3d+17) then
        tmp = a * (b * (z * -t))
    else if (j <= 1.1d+129) then
        tmp = (k * y2) * (y1 * y4)
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (j <= -2.1e+15) {
		tmp = t_1;
	} else if (j <= -1.05e-257) {
		tmp = a * (z * (t * -b));
	} else if (j <= 3.1e-220) {
		tmp = a * (y * (x * b));
	} else if (j <= 3.3e+17) {
		tmp = a * (b * (z * -t));
	} else if (j <= 1.1e+129) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (t * (b * j))
	tmp = 0
	if j <= -2.1e+15:
		tmp = t_1
	elif j <= -1.05e-257:
		tmp = a * (z * (t * -b))
	elif j <= 3.1e-220:
		tmp = a * (y * (x * b))
	elif j <= 3.3e+17:
		tmp = a * (b * (z * -t))
	elif j <= 1.1e+129:
		tmp = (k * y2) * (y1 * y4)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(t * Float64(b * j)))
	tmp = 0.0
	if (j <= -2.1e+15)
		tmp = t_1;
	elseif (j <= -1.05e-257)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (j <= 3.1e-220)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (j <= 3.3e+17)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (j <= 1.1e+129)
		tmp = Float64(Float64(k * y2) * Float64(y1 * y4));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (t * (b * j));
	tmp = 0.0;
	if (j <= -2.1e+15)
		tmp = t_1;
	elseif (j <= -1.05e-257)
		tmp = a * (z * (t * -b));
	elseif (j <= 3.1e-220)
		tmp = a * (y * (x * b));
	elseif (j <= 3.3e+17)
		tmp = a * (b * (z * -t));
	elseif (j <= 1.1e+129)
		tmp = (k * y2) * (y1 * y4);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.1e+15], t$95$1, If[LessEqual[j, -1.05e-257], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-220], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e+17], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+129], N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.1e15 or 1.1e129 < j

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 19.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 19.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 28.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 36.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.6%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 37.6%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 32.0%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if -2.1e15 < j < -1.05000000000000005e-257

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 33.3%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 33.3%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 33.3%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 33.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 31.5%

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

   8. Taylor expanded in y around 0 26.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.3%

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

      2. *-commutative 26.3%

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

      3. associate-*r* 29.9%

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

      4. distribute-rgt-neg-in 29.9%

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

   10. Simplified 29.9%

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

   if -1.05000000000000005e-257 < j < 3.10000000000000011e-220

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 41.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 41.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 41.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 28.1%

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

   8. Taylor expanded in y around inf 27.8%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if 3.10000000000000011e-220 < j < 3.3e17

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 33.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 33.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 33.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 33.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 33.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 18.6%

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

   8. Taylor expanded in y around 0 21.1%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 21.1%

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

      2. distribute-lft-neg-in 21.1%

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

      3. *-commutative 21.1%

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

   10. Simplified 21.1%

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

   if 3.3e17 < j < 1.1e129

   1. Initial program 13.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 13.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 13.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 27.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 36.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 32.2%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 32.2%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 32.2%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 32.2%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around inf 36.2%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.2%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. associate-*r* 40.1%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \cdot k \]

      3. associate-*l* 44.3%

         \[\leadsto \color{blue}{\left(y4 \cdot y1\right) \cdot \left(y2 \cdot k\right)} \]

      4. *-commutative 44.3%

         \[\leadsto \left(y4 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y2\right)} \]

      5. *-commutative 44.3%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right)} \cdot \left(k \cdot y2\right) \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \end{array} \]

Alternative 28: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.42 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (- k) (* y y4)))))
   (if (<= y4 -3.8e-15)
     t_1
     (if (<= y4 -8.4e-296)
       (* k (- (* i (* z y1))))
       (if (<= y4 1.42e-123)
         (* a (* b (* z (- t))))
         (if (<= y4 1.22e-8) (* y4 (* y1 (* j (- y3)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double tmp;
	if (y4 <= -3.8e-15) {
		tmp = t_1;
	} else if (y4 <= -8.4e-296) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 1.42e-123) {
		tmp = a * (b * (z * -t));
	} else if (y4 <= 1.22e-8) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (-k * (y * y4))
    if (y4 <= (-3.8d-15)) then
        tmp = t_1
    else if (y4 <= (-8.4d-296)) then
        tmp = k * -(i * (z * y1))
    else if (y4 <= 1.42d-123) then
        tmp = a * (b * (z * -t))
    else if (y4 <= 1.22d-8) then
        tmp = y4 * (y1 * (j * -y3))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double tmp;
	if (y4 <= -3.8e-15) {
		tmp = t_1;
	} else if (y4 <= -8.4e-296) {
		tmp = k * -(i * (z * y1));
	} else if (y4 <= 1.42e-123) {
		tmp = a * (b * (z * -t));
	} else if (y4 <= 1.22e-8) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (-k * (y * y4))
	tmp = 0
	if y4 <= -3.8e-15:
		tmp = t_1
	elif y4 <= -8.4e-296:
		tmp = k * -(i * (z * y1))
	elif y4 <= 1.42e-123:
		tmp = a * (b * (z * -t))
	elif y4 <= 1.22e-8:
		tmp = y4 * (y1 * (j * -y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(-k) * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -3.8e-15)
		tmp = t_1;
	elseif (y4 <= -8.4e-296)
		tmp = Float64(k * Float64(-Float64(i * Float64(z * y1))));
	elseif (y4 <= 1.42e-123)
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	elseif (y4 <= 1.22e-8)
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (-k * (y * y4));
	tmp = 0.0;
	if (y4 <= -3.8e-15)
		tmp = t_1;
	elseif (y4 <= -8.4e-296)
		tmp = k * -(i * (z * y1));
	elseif (y4 <= 1.42e-123)
		tmp = a * (b * (z * -t));
	elseif (y4 <= 1.22e-8)
		tmp = y4 * (y1 * (j * -y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3.8e-15], t$95$1, If[LessEqual[y4, -8.4e-296], N[(k * (-N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y4, 1.42e-123], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.22e-8], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -3.8000000000000002e-15 or 1.22e-8 < y4

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 41.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 41.7%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 41.7%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 41.7%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   if -3.8000000000000002e-15 < y4 < -8.3999999999999997e-296

   1. Initial program 22.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]

   5. Taylor expanded in k around inf 32.6%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(k \cdot \left(y1 \cdot i - y0 \cdot b\right)\right)} \cdot z\right) \]

   6. Taylor expanded in y1 around inf 21.0%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 21.0%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(i \cdot z\right) \cdot y1\right)}\right) \]

      2. associate-*r* 25.3%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(i \cdot \left(z \cdot y1\right)\right)}\right) \]

   8. Simplified 25.3%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right)\right)} \]

   if -8.3999999999999997e-296 < y4 < 1.42000000000000008e-123

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 31.4%

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

   8. Taylor expanded in y around 0 24.0%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 24.0%

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

      2. distribute-lft-neg-in 24.0%

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

      3. *-commutative 24.0%

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

   10. Simplified 24.0%

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

   if 1.42000000000000008e-123 < y4 < 1.22e-8

   1. Initial program 36.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 30.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 30.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 30.2%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 30.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 29.7%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 29.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 29.7%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 29.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 29.7%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -8.4 \cdot 10^{-296}:\\ \;\;\;\;k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.42 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 29: 22.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-144}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* t (* b j)))))
   (if (<= x -1.6e+23)
     (* a (* y (* x b)))
     (if (<= x 1.15e-281)
       t_1
       (if (<= x 2.3e-144)
         (* k (* y4 (* y1 y2)))
         (if (<= x 2.2e+126) t_1 (* a (* b (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (x <= -1.6e+23) {
		tmp = a * (y * (x * b));
	} else if (x <= 1.15e-281) {
		tmp = t_1;
	} else if (x <= 2.3e-144) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 2.2e+126) {
		tmp = t_1;
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (t * (b * j))
    if (x <= (-1.6d+23)) then
        tmp = a * (y * (x * b))
    else if (x <= 1.15d-281) then
        tmp = t_1
    else if (x <= 2.3d-144) then
        tmp = k * (y4 * (y1 * y2))
    else if (x <= 2.2d+126) then
        tmp = t_1
    else
        tmp = a * (b * (x * y))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (t * (b * j));
	double tmp;
	if (x <= -1.6e+23) {
		tmp = a * (y * (x * b));
	} else if (x <= 1.15e-281) {
		tmp = t_1;
	} else if (x <= 2.3e-144) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 2.2e+126) {
		tmp = t_1;
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (t * (b * j))
	tmp = 0
	if x <= -1.6e+23:
		tmp = a * (y * (x * b))
	elif x <= 1.15e-281:
		tmp = t_1
	elif x <= 2.3e-144:
		tmp = k * (y4 * (y1 * y2))
	elif x <= 2.2e+126:
		tmp = t_1
	else:
		tmp = a * (b * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(t * Float64(b * j)))
	tmp = 0.0
	if (x <= -1.6e+23)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 1.15e-281)
		tmp = t_1;
	elseif (x <= 2.3e-144)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (x <= 2.2e+126)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (t * (b * j));
	tmp = 0.0;
	if (x <= -1.6e+23)
		tmp = a * (y * (x * b));
	elseif (x <= 1.15e-281)
		tmp = t_1;
	elseif (x <= 2.3e-144)
		tmp = k * (y4 * (y1 * y2));
	elseif (x <= 2.2e+126)
		tmp = t_1;
	else
		tmp = a * (b * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+23], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-281], t$95$1, If[LessEqual[x, 2.3e-144], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+126], t$95$1, N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e23

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 43.1%

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

   8. Taylor expanded in y around inf 33.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -1.6e23 < x < 1.14999999999999994e-281 or 2.3e-144 < x < 2.19999999999999999e126

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 34.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 26.5%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 1.14999999999999994e-281 < x < 2.3e-144

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 27.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.1%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 27.1%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 27.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 27.8%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 27.8%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 27.8%

       \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1\right)\right)} \]

   if 2.19999999999999999e126 < x

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 26.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 26.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 26.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.9%

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

   8. Taylor expanded in y around inf 35.7%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-281}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-144}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+126}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 30: 22.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.7e+27)
   (* y4 (* y1 (* j (- y3))))
   (if (<= j -1.85e-300)
     (* a (* z (* t (- b))))
     (if (<= j 1.1e-59)
       (* c (* (* t y2) (- y4)))
       (if (<= j 5.2e+127) (* (* k y2) (* y1 y4)) (* y4 (* t (* b j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.7e+27) {
		tmp = y4 * (y1 * (j * -y3));
	} else if (j <= -1.85e-300) {
		tmp = a * (z * (t * -b));
	} else if (j <= 1.1e-59) {
		tmp = c * ((t * y2) * -y4);
	} else if (j <= 5.2e+127) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = y4 * (t * (b * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.7d+27)) then
        tmp = y4 * (y1 * (j * -y3))
    else if (j <= (-1.85d-300)) then
        tmp = a * (z * (t * -b))
    else if (j <= 1.1d-59) then
        tmp = c * ((t * y2) * -y4)
    else if (j <= 5.2d+127) then
        tmp = (k * y2) * (y1 * y4)
    else
        tmp = y4 * (t * (b * j))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.7e+27) {
		tmp = y4 * (y1 * (j * -y3));
	} else if (j <= -1.85e-300) {
		tmp = a * (z * (t * -b));
	} else if (j <= 1.1e-59) {
		tmp = c * ((t * y2) * -y4);
	} else if (j <= 5.2e+127) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = y4 * (t * (b * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.7e+27:
		tmp = y4 * (y1 * (j * -y3))
	elif j <= -1.85e-300:
		tmp = a * (z * (t * -b))
	elif j <= 1.1e-59:
		tmp = c * ((t * y2) * -y4)
	elif j <= 5.2e+127:
		tmp = (k * y2) * (y1 * y4)
	else:
		tmp = y4 * (t * (b * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.7e+27)
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	elseif (j <= -1.85e-300)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (j <= 1.1e-59)
		tmp = Float64(c * Float64(Float64(t * y2) * Float64(-y4)));
	elseif (j <= 5.2e+127)
		tmp = Float64(Float64(k * y2) * Float64(y1 * y4));
	else
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.7e+27)
		tmp = y4 * (y1 * (j * -y3));
	elseif (j <= -1.85e-300)
		tmp = a * (z * (t * -b));
	elseif (j <= 1.1e-59)
		tmp = c * ((t * y2) * -y4);
	elseif (j <= 5.2e+127)
		tmp = (k * y2) * (y1 * y4);
	else
		tmp = y4 * (t * (b * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.7e+27], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.85e-300], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e-59], N[(c * N[(N[(t * y2), $MachinePrecision] * (-y4)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e+127], N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.7e27

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 29.7%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 29.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 29.7%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 29.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 29.9%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 29.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 29.9%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 29.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 29.9%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   if -1.7e27 < j < -1.8500000000000001e-300

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 35.0%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 35.0%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 35.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 35.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 35.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 32.5%

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

   8. Taylor expanded in y around 0 21.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 21.5%

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

      2. *-commutative 21.5%

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

      3. associate-*r* 25.6%

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

      4. distribute-rgt-neg-in 25.6%

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

   10. Simplified 25.6%

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

   if -1.8500000000000001e-300 < j < 1.0999999999999999e-59

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 26.5%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 22.7%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 22.7%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 22.7%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 22.7%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 21.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 21.1%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 21.1%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

   10. Simplified 21.1%

       \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

   if 1.0999999999999999e-59 < j < 5.2000000000000004e127

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 37.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 34.1%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 34.1%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 34.1%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around inf 31.1%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \cdot k \]

      3. associate-*l* 42.2%

         \[\leadsto \color{blue}{\left(y4 \cdot y1\right) \cdot \left(y2 \cdot k\right)} \]

      4. *-commutative 42.2%

         \[\leadsto \left(y4 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y2\right)} \]

      5. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right)} \cdot \left(k \cdot y2\right) \]

   10. Simplified 42.2%

       \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2\right)} \]

   if 5.2000000000000004e127 < j

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 27.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 37.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 37.6%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \end{array} \]

Alternative 31: 21.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(y4 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= c -5e+87)
   (* (* t c) (* y4 (- y2)))
   (if (<= c -1.95e-256)
     (* a (* b (- (* x y) (* z t))))
     (if (<= c 3.1e-7)
       (* b (* (- k) (* y y4)))
       (if (<= c 1.55e+72) (* y4 (* t (* b j))) (* (* k y2) (* y1 y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (c <= -5e+87) {
		tmp = (t * c) * (y4 * -y2);
	} else if (c <= -1.95e-256) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (c <= 3.1e-7) {
		tmp = b * (-k * (y * y4));
	} else if (c <= 1.55e+72) {
		tmp = y4 * (t * (b * j));
	} else {
		tmp = (k * y2) * (y1 * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (c <= (-5d+87)) then
        tmp = (t * c) * (y4 * -y2)
    else if (c <= (-1.95d-256)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (c <= 3.1d-7) then
        tmp = b * (-k * (y * y4))
    else if (c <= 1.55d+72) then
        tmp = y4 * (t * (b * j))
    else
        tmp = (k * y2) * (y1 * y4)
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (c <= -5e+87) {
		tmp = (t * c) * (y4 * -y2);
	} else if (c <= -1.95e-256) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (c <= 3.1e-7) {
		tmp = b * (-k * (y * y4));
	} else if (c <= 1.55e+72) {
		tmp = y4 * (t * (b * j));
	} else {
		tmp = (k * y2) * (y1 * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if c <= -5e+87:
		tmp = (t * c) * (y4 * -y2)
	elif c <= -1.95e-256:
		tmp = a * (b * ((x * y) - (z * t)))
	elif c <= 3.1e-7:
		tmp = b * (-k * (y * y4))
	elif c <= 1.55e+72:
		tmp = y4 * (t * (b * j))
	else:
		tmp = (k * y2) * (y1 * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (c <= -5e+87)
		tmp = Float64(Float64(t * c) * Float64(y4 * Float64(-y2)));
	elseif (c <= -1.95e-256)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (c <= 3.1e-7)
		tmp = Float64(b * Float64(Float64(-k) * Float64(y * y4)));
	elseif (c <= 1.55e+72)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	else
		tmp = Float64(Float64(k * y2) * Float64(y1 * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (c <= -5e+87)
		tmp = (t * c) * (y4 * -y2);
	elseif (c <= -1.95e-256)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (c <= 3.1e-7)
		tmp = b * (-k * (y * y4));
	elseif (c <= 1.55e+72)
		tmp = y4 * (t * (b * j));
	else
		tmp = (k * y2) * (y1 * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[c, -5e+87], N[(N[(t * c), $MachinePrecision] * N[(y4 * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.95e-256], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e-7], N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e+72], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.9999999999999998e87

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 37.9%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 37.9%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 37.9%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around 0 36.3%

      \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(-1 \cdot \left(c \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 36.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(-c \cdot t\right)} \]

      2. *-commutative 36.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(-\color{blue}{t \cdot c}\right) \]

      3. distribute-rgt-neg-in 36.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(t \cdot \left(-c\right)\right)} \]

   10. Simplified 36.3%

       \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(t \cdot \left(-c\right)\right)} \]

   if -4.9999999999999998e87 < c < -1.9499999999999999e-256

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 49.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 49.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 49.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 49.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 39.5%

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

   if -1.9499999999999999e-256 < c < 3.1e-7

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 31.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 31.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 35.8%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 32.0%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 32.0%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 32.0%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 32.0%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   if 3.1e-7 < c < 1.54999999999999994e72

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 29.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 34.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 34.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 39.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 1.54999999999999994e72 < c

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 27.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 25.3%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 25.3%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 25.3%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 25.3%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around inf 23.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 23.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. associate-*r* 28.3%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \cdot k \]

      3. associate-*l* 33.0%

         \[\leadsto \color{blue}{\left(y4 \cdot y1\right) \cdot \left(y2 \cdot k\right)} \]

      4. *-commutative 33.0%

         \[\leadsto \left(y4 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y2\right)} \]

      5. *-commutative 33.0%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right)} \cdot \left(k \cdot y2\right) \]

   10. Simplified 33.0%

       \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(y4 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \end{array} \]

Alternative 32: 21.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-11}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (- k) (* y y4)))))
   (if (<= y4 -2.3e+17)
     t_1
     (if (<= y4 1.7e-143)
       (* a (* b (* x y)))
       (if (<= y4 7.4e-11) (* y4 (* y1 (* j (- y3)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double tmp;
	if (y4 <= -2.3e+17) {
		tmp = t_1;
	} else if (y4 <= 1.7e-143) {
		tmp = a * (b * (x * y));
	} else if (y4 <= 7.4e-11) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (-k * (y * y4))
    if (y4 <= (-2.3d+17)) then
        tmp = t_1
    else if (y4 <= 1.7d-143) then
        tmp = a * (b * (x * y))
    else if (y4 <= 7.4d-11) then
        tmp = y4 * (y1 * (j * -y3))
    else
        tmp = t_1
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-k * (y * y4));
	double tmp;
	if (y4 <= -2.3e+17) {
		tmp = t_1;
	} else if (y4 <= 1.7e-143) {
		tmp = a * (b * (x * y));
	} else if (y4 <= 7.4e-11) {
		tmp = y4 * (y1 * (j * -y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (-k * (y * y4))
	tmp = 0
	if y4 <= -2.3e+17:
		tmp = t_1
	elif y4 <= 1.7e-143:
		tmp = a * (b * (x * y))
	elif y4 <= 7.4e-11:
		tmp = y4 * (y1 * (j * -y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(-k) * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -2.3e+17)
		tmp = t_1;
	elseif (y4 <= 1.7e-143)
		tmp = Float64(a * Float64(b * Float64(x * y)));
	elseif (y4 <= 7.4e-11)
		tmp = Float64(y4 * Float64(y1 * Float64(j * Float64(-y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (-k * (y * y4));
	tmp = 0.0;
	if (y4 <= -2.3e+17)
		tmp = t_1;
	elseif (y4 <= 1.7e-143)
		tmp = a * (b * (x * y));
	elseif (y4 <= 7.4e-11)
		tmp = y4 * (y1 * (j * -y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[((-k) * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.3e+17], t$95$1, If[LessEqual[y4, 1.7e-143], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.4e-11], N[(y4 * N[(y1 * N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -2.3e17 or 7.4000000000000003e-11 < y4

   1. Initial program 17.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 17.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 17.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around 0 42.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot y\right)\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto \color{blue}{\left(-k \cdot \left(y4 \cdot y\right)\right)} \cdot b \]

      2. *-commutative 42.3%

         \[\leadsto \left(-\color{blue}{\left(y4 \cdot y\right) \cdot k}\right) \cdot b \]

      3. distribute-rgt-neg-in 42.3%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot y\right) \cdot \left(-k\right)\right)} \cdot b \]

   if -2.3e17 < y4 < 1.69999999999999992e-143

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 37.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 37.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 37.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 37.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 26.8%

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

   8. Taylor expanded in y around inf 20.7%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   if 1.69999999999999992e-143 < y4 < 7.4000000000000003e-11

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 40.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 40.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 25.5%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.5%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 25.5%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 25.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around 0 25.1%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot \left(y3 \cdot j\right)\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 25.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-y3 \cdot j\right)} \cdot y1\right) \]

      2. *-commutative 25.1%

         \[\leadsto y4 \cdot \left(\left(-\color{blue}{j \cdot y3}\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in 25.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]

   10. Simplified 25.1%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(j \cdot \left(-y3\right)\right)} \cdot y1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-11}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(j \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(-k\right) \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 33: 22.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-281}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+125}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -5.5e+26)
   (* a (* y (* x b)))
   (if (<= x 5.3e-281)
     (* y4 (* t (* b j)))
     (if (<= x 3.3e+125) (* y4 (* y1 (* k y2))) (* a (* b (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -5.5e+26) {
		tmp = a * (y * (x * b));
	} else if (x <= 5.3e-281) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3.3e+125) {
		tmp = y4 * (y1 * (k * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-5.5d+26)) then
        tmp = a * (y * (x * b))
    else if (x <= 5.3d-281) then
        tmp = y4 * (t * (b * j))
    else if (x <= 3.3d+125) then
        tmp = y4 * (y1 * (k * y2))
    else
        tmp = a * (b * (x * y))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -5.5e+26) {
		tmp = a * (y * (x * b));
	} else if (x <= 5.3e-281) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 3.3e+125) {
		tmp = y4 * (y1 * (k * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -5.5e+26:
		tmp = a * (y * (x * b))
	elif x <= 5.3e-281:
		tmp = y4 * (t * (b * j))
	elif x <= 3.3e+125:
		tmp = y4 * (y1 * (k * y2))
	else:
		tmp = a * (b * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -5.5e+26)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 5.3e-281)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 3.3e+125)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	else
		tmp = Float64(a * Float64(b * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -5.5e+26)
		tmp = a * (y * (x * b));
	elseif (x <= 5.3e-281)
		tmp = y4 * (t * (b * j));
	elseif (x <= 3.3e+125)
		tmp = y4 * (y1 * (k * y2));
	else
		tmp = a * (b * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -5.5e+26], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e-281], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+125], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.4999999999999997e26

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 43.1%

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

   8. Taylor expanded in y around inf 33.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -5.4999999999999997e26 < x < 5.29999999999999995e-281

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 36.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 36.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 28.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 5.29999999999999995e-281 < x < 3.30000000000000005e125

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 28.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 27.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 27.3%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 27.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 22.3%

      \[\leadsto y4 \cdot \left(\color{blue}{\left(k \cdot y2\right)} \cdot y1\right) \]
   9. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot k\right)} \cdot y1\right) \]

   10. Simplified 22.3%

       \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot k\right)} \cdot y1\right) \]

   if 3.30000000000000005e125 < x

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 26.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 26.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 26.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.9%

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

   8. Taylor expanded in y around inf 35.7%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-281}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+125}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 34: 21.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-308}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+126}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.1e+17)
   (* a (* y (* x b)))
   (if (<= x 7.4e-308)
     (* y4 (* t (* b j)))
     (if (<= x 1.85e+126) (* (* k y2) (* y1 y4)) (* a (* b (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+17) {
		tmp = a * (y * (x * b));
	} else if (x <= 7.4e-308) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 1.85e+126) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.1d+17)) then
        tmp = a * (y * (x * b))
    else if (x <= 7.4d-308) then
        tmp = y4 * (t * (b * j))
    else if (x <= 1.85d+126) then
        tmp = (k * y2) * (y1 * y4)
    else
        tmp = a * (b * (x * y))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+17) {
		tmp = a * (y * (x * b));
	} else if (x <= 7.4e-308) {
		tmp = y4 * (t * (b * j));
	} else if (x <= 1.85e+126) {
		tmp = (k * y2) * (y1 * y4);
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.1e+17:
		tmp = a * (y * (x * b))
	elif x <= 7.4e-308:
		tmp = y4 * (t * (b * j))
	elif x <= 1.85e+126:
		tmp = (k * y2) * (y1 * y4)
	else:
		tmp = a * (b * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.1e+17)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 7.4e-308)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (x <= 1.85e+126)
		tmp = Float64(Float64(k * y2) * Float64(y1 * y4));
	else
		tmp = Float64(a * Float64(b * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.1e+17)
		tmp = a * (y * (x * b));
	elseif (x <= 7.4e-308)
		tmp = y4 * (t * (b * j));
	elseif (x <= 1.85e+126)
		tmp = (k * y2) * (y1 * y4);
	else
		tmp = a * (b * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.1e+17], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-308], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+126], N[(N[(k * y2), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1e17

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 43.1%

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

   8. Taylor expanded in y around inf 33.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -1.1e17 < x < 7.40000000000000012e-308

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.4%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right) \cdot b} \]

   8. Taylor expanded in t around inf 28.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b\right)\right)} \]

   if 7.40000000000000012e-308 < x < 1.8499999999999999e126

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 28.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 24.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 22.4%

         \[\leadsto \color{blue}{\left(y4 \cdot y2\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

      2. *-commutative 22.4%

         \[\leadsto \color{blue}{\left(y2 \cdot y4\right)} \cdot \left(k \cdot y1 - c \cdot t\right) \]

      3. *-commutative 22.4%

         \[\leadsto \left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - \color{blue}{t \cdot c}\right) \]

   7. Simplified 22.4%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - t \cdot c\right)} \]

   8. Taylor expanded in k around inf 18.8%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 18.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. associate-*r* 20.7%

         \[\leadsto \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \cdot k \]

      3. associate-*l* 23.5%

         \[\leadsto \color{blue}{\left(y4 \cdot y1\right) \cdot \left(y2 \cdot k\right)} \]

      4. *-commutative 23.5%

         \[\leadsto \left(y4 \cdot y1\right) \cdot \color{blue}{\left(k \cdot y2\right)} \]

      5. *-commutative 23.5%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right)} \cdot \left(k \cdot y2\right) \]

   10. Simplified 23.5%

       \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2\right)} \]

   if 1.8499999999999999e126 < x

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 26.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 26.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 26.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.9%

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

   8. Taylor expanded in y around inf 35.7%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-308}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+126}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 35: 21.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0034:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+126}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -0.0034)
   (* a (* y (* x b)))
   (if (<= x 1.4e+126) (* k (* y4 (* y1 y2))) (* a (* b (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -0.0034) {
		tmp = a * (y * (x * b));
	} else if (x <= 1.4e+126) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-0.0034d0)) then
        tmp = a * (y * (x * b))
    else if (x <= 1.4d+126) then
        tmp = k * (y4 * (y1 * y2))
    else
        tmp = a * (b * (x * y))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -0.0034) {
		tmp = a * (y * (x * b));
	} else if (x <= 1.4e+126) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -0.0034:
		tmp = a * (y * (x * b))
	elif x <= 1.4e+126:
		tmp = k * (y4 * (y1 * y2))
	else:
		tmp = a * (b * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -0.0034)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 1.4e+126)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	else
		tmp = Float64(a * Float64(b * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -0.0034)
		tmp = a * (y * (x * b));
	elseif (x <= 1.4e+126)
		tmp = k * (y4 * (y1 * y2));
	else
		tmp = a * (b * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -0.0034], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+126], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00339999999999999981

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.6%

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

   8. Taylor expanded in y around inf 31.9%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -0.00339999999999999981 < x < 1.40000000000000005e126

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 28.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 28.9%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 28.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 19.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 19.6%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 19.6%

       \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1\right)\right)} \]

   if 1.40000000000000005e126 < x

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 26.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 26.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 26.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.9%

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

   8. Taylor expanded in y around inf 35.7%

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

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0034:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+126}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 36: 21.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00265:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+126}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -0.00265)
   (* a (* y (* x b)))
   (if (<= x 4.4e+126) (* y4 (* k (* y1 y2))) (* a (* b (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -0.00265) {
		tmp = a * (y * (x * b));
	} else if (x <= 4.4e+126) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-0.00265d0)) then
        tmp = a * (y * (x * b))
    else if (x <= 4.4d+126) then
        tmp = y4 * (k * (y1 * y2))
    else
        tmp = a * (b * (x * y))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -0.00265) {
		tmp = a * (y * (x * b));
	} else if (x <= 4.4e+126) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = a * (b * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -0.00265:
		tmp = a * (y * (x * b))
	elif x <= 4.4e+126:
		tmp = y4 * (k * (y1 * y2))
	else:
		tmp = a * (b * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -0.00265)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (x <= 4.4e+126)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	else
		tmp = Float64(a * Float64(b * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -0.00265)
		tmp = a * (y * (x * b));
	elseif (x <= 4.4e+126)
		tmp = y4 * (k * (y1 * y2));
	else
		tmp = a * (b * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -0.00265], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+126], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00265000000000000001

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 42.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.6%

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

   8. Taylor expanded in y around inf 31.9%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -0.00265000000000000001 < x < 4.39999999999999997e126

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 32.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 28.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) \]

      2. *-commutative 28.9%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   7. Simplified 28.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) \cdot y1\right)} \]

   8. Taylor expanded in k around inf 19.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 19.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 19.7%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if 4.39999999999999997e126 < x

   1. Initial program 14.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 26.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 26.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 26.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 26.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 30.9%

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

   8. Taylor expanded in y around inf 35.7%

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

4. Final simplification 25.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00265:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+126}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 37: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot \left(x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* b (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (b * (x * y));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (b * (x * y))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (b * (x * y));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (b * (x * y))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(b * Float64(x * y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (b * (x * y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(b * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 23.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Step-by-step derivation

   1. associate-+l- 23.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

3. Simplified 23.5%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in a around inf 35.3%

   \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
5. Step-by-step derivation

   1. associate--l+ 35.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

   2. mul-1-neg 35.3%

      \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

   3. mul-1-neg 35.3%

      \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

6. Simplified 35.3%

   \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

7. Taylor expanded in b around inf 25.2%

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

8. Taylor expanded in y around inf 17.3%

   \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

9. Final simplification 17.3%

   \[\leadsto a \cdot \left(b \cdot \left(x \cdot y\right)\right) \]

Developer target: 28.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))