Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.1% → 38.1%

Time: 1.1min

Alternatives: 38

Speedup: 2.6×

• 89.0% 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: 30.1% 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: 38.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := y2 \cdot t\_2 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\\ t_4 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;y4 \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;k \cdot t\_3\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{-122}:\\ \;\;\;\;y3 \cdot \left(y \cdot t\_4 - \left(j \cdot t\_2 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-142}:\\ \;\;\;\;k \cdot \left(t\_3 + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t\_1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 6.4 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot t\_1\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 3.9 \cdot 10^{+211}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+283}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot t\_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (+ (* y2 t_2) (* y (- (* i y5) (* b y4)))))
        (t_4 (- (* c y4) (* a y5))))
   (if (<= y4 -6.5e+149)
     (*
      y4
      (+
       (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
       (* c (- (* y y3) (* t y2)))))
     (if (<= y4 -1.15e+33)
       (* k t_3)
       (if (<= y4 -8.2e-122)
         (* y3 (- (* y t_4) (+ (* j t_2) (* z (- (* c y0) (* a y1))))))
         (if (<= y4 -2e-142)
           (* k (+ t_3 (* z (- (* b y0) (* i y1)))))
           (if (<= y4 1.9e-196)
             (*
              y5
              (+
               (* a (- (* t y2) (* y y3)))
               (+ (* i (- (* y k) (* t j))) (* y0 t_1))))
             (if (<= y4 2.9e-55)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= y4 6.4e+53)
                 (*
                  j
                  (+
                   (+
                    (* t (- (* b y4) (* i y5)))
                    (* y3 (- (* y0 y5) (* y1 y4))))
                   (* x (- (* i y1) (* b y0)))))
                 (if (<= y4 2.1e+185)
                   (*
                    y0
                    (+
                     (+ (* c (- (* x y2) (* z y3))) (* y5 t_1))
                     (* b (- (* z k) (* x j)))))
                   (if (<= y4 3.9e+211)
                     (* t (* z (- (* c i) (* a b))))
                     (if (<= y4 1.6e+283)
                       (* c (* y (* y3 y4)))
                       (-
                        (* x (* y (- (* a b) (* c i))))
                        (* t (* y2 t_4)))))))))))))))

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 = (j * y3) - (k * y2);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (y2 * t_2) + (y * ((i * y5) - (b * y4)));
	double t_4 = (c * y4) - (a * y5);
	double tmp;
	if (y4 <= -6.5e+149) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -1.15e+33) {
		tmp = k * t_3;
	} else if (y4 <= -8.2e-122) {
		tmp = y3 * ((y * t_4) - ((j * t_2) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2e-142) {
		tmp = k * (t_3 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.9e-196) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	} else if (y4 <= 2.9e-55) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 6.4e+53) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y4 <= 2.1e+185) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_1)) + (b * ((z * k) - (x * j))));
	} else if (y4 <= 3.9e+211) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 1.6e+283) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * t_4));
	}
	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 = (j * y3) - (k * y2)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = (y2 * t_2) + (y * ((i * y5) - (b * y4)))
    t_4 = (c * y4) - (a * y5)
    if (y4 <= (-6.5d+149)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y4 <= (-1.15d+33)) then
        tmp = k * t_3
    else if (y4 <= (-8.2d-122)) then
        tmp = y3 * ((y * t_4) - ((j * t_2) + (z * ((c * y0) - (a * y1)))))
    else if (y4 <= (-2d-142)) then
        tmp = k * (t_3 + (z * ((b * y0) - (i * y1))))
    else if (y4 <= 1.9d-196) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
    else if (y4 <= 2.9d-55) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y4 <= 6.4d+53) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (y4 <= 2.1d+185) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_1)) + (b * ((z * k) - (x * j))))
    else if (y4 <= 3.9d+211) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y4 <= 1.6d+283) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * t_4))
    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 = (j * y3) - (k * y2);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (y2 * t_2) + (y * ((i * y5) - (b * y4)));
	double t_4 = (c * y4) - (a * y5);
	double tmp;
	if (y4 <= -6.5e+149) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -1.15e+33) {
		tmp = k * t_3;
	} else if (y4 <= -8.2e-122) {
		tmp = y3 * ((y * t_4) - ((j * t_2) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2e-142) {
		tmp = k * (t_3 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.9e-196) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	} else if (y4 <= 2.9e-55) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 6.4e+53) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y4 <= 2.1e+185) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_1)) + (b * ((z * k) - (x * j))));
	} else if (y4 <= 3.9e+211) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y4 <= 1.6e+283) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * t_4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y3) - (k * y2)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = (y2 * t_2) + (y * ((i * y5) - (b * y4)))
	t_4 = (c * y4) - (a * y5)
	tmp = 0
	if y4 <= -6.5e+149:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y4 <= -1.15e+33:
		tmp = k * t_3
	elif y4 <= -8.2e-122:
		tmp = y3 * ((y * t_4) - ((j * t_2) + (z * ((c * y0) - (a * y1)))))
	elif y4 <= -2e-142:
		tmp = k * (t_3 + (z * ((b * y0) - (i * y1))))
	elif y4 <= 1.9e-196:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
	elif y4 <= 2.9e-55:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y4 <= 6.4e+53:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif y4 <= 2.1e+185:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_1)) + (b * ((z * k) - (x * j))))
	elif y4 <= 3.9e+211:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y4 <= 1.6e+283:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * t_4))
	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(j * y3) - Float64(k * y2))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(y2 * t_2) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	t_4 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (y4 <= -6.5e+149)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y4 <= -1.15e+33)
		tmp = Float64(k * t_3);
	elseif (y4 <= -8.2e-122)
		tmp = Float64(y3 * Float64(Float64(y * t_4) - Float64(Float64(j * t_2) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y4 <= -2e-142)
		tmp = Float64(k * Float64(t_3 + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 1.9e-196)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_1))));
	elseif (y4 <= 2.9e-55)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y4 <= 6.4e+53)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y4 <= 2.1e+185)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * t_1)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y4 <= 3.9e+211)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y4 <= 1.6e+283)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) - Float64(t * Float64(y2 * t_4)));
	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 = (j * y3) - (k * y2);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = (y2 * t_2) + (y * ((i * y5) - (b * y4)));
	t_4 = (c * y4) - (a * y5);
	tmp = 0.0;
	if (y4 <= -6.5e+149)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y4 <= -1.15e+33)
		tmp = k * t_3;
	elseif (y4 <= -8.2e-122)
		tmp = y3 * ((y * t_4) - ((j * t_2) + (z * ((c * y0) - (a * y1)))));
	elseif (y4 <= -2e-142)
		tmp = k * (t_3 + (z * ((b * y0) - (i * y1))));
	elseif (y4 <= 1.9e-196)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	elseif (y4 <= 2.9e-55)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y4 <= 6.4e+53)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (y4 <= 2.1e+185)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_1)) + (b * ((z * k) - (x * j))));
	elseif (y4 <= 3.9e+211)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y4 <= 1.6e+283)
		tmp = c * (y * (y3 * y4));
	else
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * t_4));
	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[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t$95$2), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.5e+149], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.15e+33], N[(k * t$95$3), $MachinePrecision], If[LessEqual[y4, -8.2e-122], N[(y3 * N[(N[(y * t$95$4), $MachinePrecision] - N[(N[(j * t$95$2), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2e-142], N[(k * N[(t$95$3 + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.9e-196], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.9e-55], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.4e+53], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.1e+185], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.9e+211], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.6e+283], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y4 < -6.50000000000000015e149

   1. Initial program 22.0%

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

   3. Taylor expanded in y4 around inf 58.7%

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

   if -6.50000000000000015e149 < y4 < -1.15000000000000005e33

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 37.1%

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

      1. +-commutative 37.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 37.1%

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

      3. unsub-neg 37.1%

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

      4. *-commutative 37.1%

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

      5. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in k around inf 58.2%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -1.15000000000000005e33 < y4 < -8.2000000000000001e-122

   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. Add Preprocessing

   3. Taylor expanded in y3 around -inf 63.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -8.2000000000000001e-122 < y4 < -2.0000000000000001e-142

   1. Initial program 38.1%

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

   3. Taylor expanded in k around inf 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -2.0000000000000001e-142 < y4 < 1.9000000000000001e-196

   1. Initial program 37.2%

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

   3. Taylor expanded in y5 around -inf 61.3%

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

   if 1.9000000000000001e-196 < y4 < 2.9e-55

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 40.3%

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

      1. associate-*r* 40.3%

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

      2. neg-mul-1 40.3%

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

      3. +-commutative 40.3%

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

      4. mul-1-neg 40.3%

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

      5. unsub-neg 40.3%

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

      6. *-commutative 40.3%

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

      7. *-commutative 40.3%

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

      8. *-commutative 40.3%

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

      9. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in i around -inf 56.3%

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

   if 2.9e-55 < y4 < 6.4e53

   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. Add Preprocessing

   3. Taylor expanded in j around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if 6.4e53 < y4 < 2.1e185

   1. Initial program 40.7%

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

   3. Taylor expanded in y0 around inf 56.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 56.1%

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

      3. unsub-neg 56.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 56.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 56.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 56.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   if 2.1e185 < y4 < 3.90000000000000023e211

   1. Initial program 14.3%

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

   3. Taylor expanded in t around inf 42.9%

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

      1. +-commutative 42.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in z around inf 71.7%

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

   if 3.90000000000000023e211 < y4 < 1.60000000000000005e283

   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. Add Preprocessing

   3. Taylor expanded in y around inf 36.4%

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

      1. +-commutative 36.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 36.4%

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

      3. unsub-neg 36.4%

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

      4. *-commutative 36.4%

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

      5. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in k around 0 18.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 55.0%

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

      1. associate-*r* 55.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 55.0%

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

      3. *-commutative 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in y around inf 81.8%

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

   if 1.60000000000000005e283 < y4

   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. Add Preprocessing

   3. Taylor expanded in y around inf 16.7%

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

      1. +-commutative 16.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 16.7%

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

      3. unsub-neg 16.7%

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

      4. *-commutative 16.7%

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

      5. *-commutative 16.7%

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

   5. Simplified 16.7%

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

   6. Taylor expanded in k around 0 33.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y3 around 0 83.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{-122}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-142}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 6.4 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 3.9 \cdot 10^{+211}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+283}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

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)) (- (* 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_1 INFINITY) t_1 (* t (* z (- (* c i) (* a b)))))))

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)) * ((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_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	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)) * ((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_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	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)) * ((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_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	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(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * 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_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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)) * ((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_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * (z * ((c * i) - (a * b)));
	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[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * 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$1, Infinity], t$95$1, N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $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 91.7%

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

   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. Add Preprocessing

   3. Taylor expanded in t around inf 22.9%

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

      1. +-commutative 22.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 22.9%

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

      3. unsub-neg 22.9%

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

      4. *-commutative 22.9%

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

      5. *-commutative 22.9%

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

   5. Simplified 22.9%

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

   6. Taylor expanded in z around inf 38.1%

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

4. Final simplification 54.6%

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

Alternative 3: 35.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := z \cdot \left(c \cdot i - a \cdot b\right)\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := t\_1 \cdot t\_3\\ t_5 := t \cdot y2 - y \cdot y3\\ t_6 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y4 \leq -7.5 \cdot 10^{+189}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;t\_4 + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + t\_2\right) + y2 \cdot t\_6\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right) + t\_5 \cdot t\_6\\ \mathbf{elif}\;y4 \leq -2.45 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right) + \frac{y0 \cdot \left(c \cdot \left(x \cdot y2\right) - \left(b \cdot \left(x \cdot j\right) + y5 \cdot t\_1\right)\right)}{z}\right)\\ \mathbf{elif}\;y4 \leq -1.7 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t\_3 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-143}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_3 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-194}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_5 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;t\_4 + b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot 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 (- (* k y2) (* j y3)))
        (t_2 (* z (- (* c i) (* a b))))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (* t_1 t_3))
        (t_5 (- (* t y2) (* y y3)))
        (t_6 (- (* a y5) (* c y4))))
   (if (<= y4 -7.5e+189)
     (* (* c y4) (- (* y y3) (* t y2)))
     (if (<= y4 -6.2e+63)
       (+ t_4 (* t (+ (+ (* j (- (* b y4) (* i y5))) t_2) (* y2 t_6))))
       (if (<= y4 -4.2e-10)
         (+
          (+
           (* x (* y (- (* a b) (* c i))))
           (* j (* y3 (- (* y0 y5) (* y1 y4)))))
          (* t_5 t_6))
         (if (<= y4 -2.45e-53)
           (*
            z
            (+
             (* y0 (- (* b k) (* c y3)))
             (/ (* y0 (- (* c (* x y2)) (+ (* b (* x j)) (* y5 t_1)))) z)))
           (if (<= y4 -1.7e-120)
             (*
              y3
              (-
               (* y (- (* c y4) (* a y5)))
               (+ (* j t_3) (* z (- (* c y0) (* a y1))))))
             (if (<= y4 -1.85e-143)
               (*
                k
                (+
                 (+ (* y2 t_3) (* y (- (* i y5) (* b y4))))
                 (* z (- (* b y0) (* i y1)))))
               (if (<= y4 1.8e-194)
                 (*
                  y5
                  (+
                   (* a t_5)
                   (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
                 (if (<= y4 7.2e-65)
                   (* i (* y1 (- (* x j) (* z k))))
                   (if (<= y4 1.1e+171)
                     (+
                      t_4
                      (*
                       b
                       (+
                        (+
                         (* a (- (* x y) (* z t)))
                         (* y4 (- (* t j) (* y k))))
                        (* y0 (- (* z k) (* x j))))))
                     (* t 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 = (k * y2) - (j * y3);
	double t_2 = z * ((c * i) - (a * b));
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = t_1 * t_3;
	double t_5 = (t * y2) - (y * y3);
	double t_6 = (a * y5) - (c * y4);
	double tmp;
	if (y4 <= -7.5e+189) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (y4 <= -6.2e+63) {
		tmp = t_4 + (t * (((j * ((b * y4) - (i * y5))) + t_2) + (y2 * t_6)));
	} else if (y4 <= -4.2e-10) {
		tmp = ((x * (y * ((a * b) - (c * i)))) + (j * (y3 * ((y0 * y5) - (y1 * y4))))) + (t_5 * t_6);
	} else if (y4 <= -2.45e-53) {
		tmp = z * ((y0 * ((b * k) - (c * y3))) + ((y0 * ((c * (x * y2)) - ((b * (x * j)) + (y5 * t_1)))) / z));
	} else if (y4 <= -1.7e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -1.85e-143) {
		tmp = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.8e-194) {
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 7.2e-65) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.1e+171) {
		tmp = t_4 + (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j)))));
	} else {
		tmp = t * 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = z * ((c * i) - (a * b))
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = t_1 * t_3
    t_5 = (t * y2) - (y * y3)
    t_6 = (a * y5) - (c * y4)
    if (y4 <= (-7.5d+189)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (y4 <= (-6.2d+63)) then
        tmp = t_4 + (t * (((j * ((b * y4) - (i * y5))) + t_2) + (y2 * t_6)))
    else if (y4 <= (-4.2d-10)) then
        tmp = ((x * (y * ((a * b) - (c * i)))) + (j * (y3 * ((y0 * y5) - (y1 * y4))))) + (t_5 * t_6)
    else if (y4 <= (-2.45d-53)) then
        tmp = z * ((y0 * ((b * k) - (c * y3))) + ((y0 * ((c * (x * y2)) - ((b * (x * j)) + (y5 * t_1)))) / z))
    else if (y4 <= (-1.7d-120)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
    else if (y4 <= (-1.85d-143)) then
        tmp = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (y4 <= 1.8d-194) then
        tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y4 <= 7.2d-65) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y4 <= 1.1d+171) then
        tmp = t_4 + (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j)))))
    else
        tmp = t * 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 = (k * y2) - (j * y3);
	double t_2 = z * ((c * i) - (a * b));
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = t_1 * t_3;
	double t_5 = (t * y2) - (y * y3);
	double t_6 = (a * y5) - (c * y4);
	double tmp;
	if (y4 <= -7.5e+189) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (y4 <= -6.2e+63) {
		tmp = t_4 + (t * (((j * ((b * y4) - (i * y5))) + t_2) + (y2 * t_6)));
	} else if (y4 <= -4.2e-10) {
		tmp = ((x * (y * ((a * b) - (c * i)))) + (j * (y3 * ((y0 * y5) - (y1 * y4))))) + (t_5 * t_6);
	} else if (y4 <= -2.45e-53) {
		tmp = z * ((y0 * ((b * k) - (c * y3))) + ((y0 * ((c * (x * y2)) - ((b * (x * j)) + (y5 * t_1)))) / z));
	} else if (y4 <= -1.7e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -1.85e-143) {
		tmp = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.8e-194) {
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 7.2e-65) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.1e+171) {
		tmp = t_4 + (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j)))));
	} else {
		tmp = t * 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 = (k * y2) - (j * y3)
	t_2 = z * ((c * i) - (a * b))
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = t_1 * t_3
	t_5 = (t * y2) - (y * y3)
	t_6 = (a * y5) - (c * y4)
	tmp = 0
	if y4 <= -7.5e+189:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif y4 <= -6.2e+63:
		tmp = t_4 + (t * (((j * ((b * y4) - (i * y5))) + t_2) + (y2 * t_6)))
	elif y4 <= -4.2e-10:
		tmp = ((x * (y * ((a * b) - (c * i)))) + (j * (y3 * ((y0 * y5) - (y1 * y4))))) + (t_5 * t_6)
	elif y4 <= -2.45e-53:
		tmp = z * ((y0 * ((b * k) - (c * y3))) + ((y0 * ((c * (x * y2)) - ((b * (x * j)) + (y5 * t_1)))) / z))
	elif y4 <= -1.7e-120:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
	elif y4 <= -1.85e-143:
		tmp = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif y4 <= 1.8e-194:
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y4 <= 7.2e-65:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y4 <= 1.1e+171:
		tmp = t_4 + (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j)))))
	else:
		tmp = t * 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(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(z * Float64(Float64(c * i) - Float64(a * b)))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(Float64(t * y2) - Float64(y * y3))
	t_6 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y4 <= -7.5e+189)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (y4 <= -6.2e+63)
		tmp = Float64(t_4 + Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + t_2) + Float64(y2 * t_6))));
	elseif (y4 <= -4.2e-10)
		tmp = Float64(Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))))) + Float64(t_5 * t_6));
	elseif (y4 <= -2.45e-53)
		tmp = Float64(z * Float64(Float64(y0 * Float64(Float64(b * k) - Float64(c * y3))) + Float64(Float64(y0 * Float64(Float64(c * Float64(x * y2)) - Float64(Float64(b * Float64(x * j)) + Float64(y5 * t_1)))) / z)));
	elseif (y4 <= -1.7e-120)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_3) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y4 <= -1.85e-143)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_3) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 1.8e-194)
		tmp = Float64(y5 * Float64(Float64(a * t_5) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y4 <= 7.2e-65)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y4 <= 1.1e+171)
		tmp = Float64(t_4 + Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))));
	else
		tmp = Float64(t * 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 = (k * y2) - (j * y3);
	t_2 = z * ((c * i) - (a * b));
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = t_1 * t_3;
	t_5 = (t * y2) - (y * y3);
	t_6 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y4 <= -7.5e+189)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (y4 <= -6.2e+63)
		tmp = t_4 + (t * (((j * ((b * y4) - (i * y5))) + t_2) + (y2 * t_6)));
	elseif (y4 <= -4.2e-10)
		tmp = ((x * (y * ((a * b) - (c * i)))) + (j * (y3 * ((y0 * y5) - (y1 * y4))))) + (t_5 * t_6);
	elseif (y4 <= -2.45e-53)
		tmp = z * ((y0 * ((b * k) - (c * y3))) + ((y0 * ((c * (x * y2)) - ((b * (x * j)) + (y5 * t_1)))) / z));
	elseif (y4 <= -1.7e-120)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	elseif (y4 <= -1.85e-143)
		tmp = k * (((y2 * t_3) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (y4 <= 1.8e-194)
		tmp = y5 * ((a * t_5) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y4 <= 7.2e-65)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y4 <= 1.1e+171)
		tmp = t_4 + (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j)))));
	else
		tmp = t * 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[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -7.5e+189], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.2e+63], N[(t$95$4 + N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.2e-10], N[(N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.45e-53], N[(z * N[(N[(y0 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(x * j), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.7e-120], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.85e-143], N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.8e-194], N[(y5 * N[(N[(a * t$95$5), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.2e-65], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.1e+171], N[(t$95$4 + N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * t$95$2), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y4 < -7.49999999999999955e189

   1. Initial program 14.4%

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

   3. Taylor expanded in y around inf 25.1%

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

      1. +-commutative 25.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 25.1%

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

      3. unsub-neg 25.1%

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

      4. *-commutative 25.1%

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

      5. *-commutative 25.1%

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

   5. Simplified 25.1%

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

   6. Taylor expanded in k around 0 32.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 54.1%

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

      1. associate-*r* 54.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 54.1%

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

      3. *-commutative 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in c around inf 61.5%

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

       1. associate-*r* 61.4%

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

       2. *-commutative 61.4%

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

       3. *-commutative 61.4%

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

       4. *-commutative 61.4%

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

   12. Simplified 61.4%

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

   if -7.49999999999999955e189 < y4 < -6.2000000000000001e63

   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. Add Preprocessing

   3. Taylor expanded in t around inf 59.3%

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

      1. +-commutative 59.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

      5. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   if -6.2000000000000001e63 < y4 < -4.2e-10

   1. Initial program 23.1%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in k around 0 77.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   if -4.2e-10 < y4 < -2.44999999999999981e-53

   1. Initial program 14.3%

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

   3. Taylor expanded in y0 around inf 57.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 57.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 57.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 57.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 57.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 57.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{z \cdot \left(y0 \cdot \left(-1 \cdot \left(c \cdot y3\right) - -1 \cdot \left(b \cdot k\right)\right) + \frac{y0 \cdot \left(c \cdot \left(x \cdot y2\right) - \left(b \cdot \left(j \cdot x\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}{z}\right)} \]

   if -2.44999999999999981e-53 < y4 < -1.70000000000000005e-120

   1. Initial program 24.9%

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

   3. Taylor expanded in y3 around -inf 83.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -1.70000000000000005e-120 < y4 < -1.85e-143

   1. Initial program 38.1%

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

   3. Taylor expanded in k around inf 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -1.85e-143 < y4 < 1.8e-194

   1. Initial program 37.2%

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

   3. Taylor expanded in y5 around -inf 61.3%

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

   if 1.8e-194 < y4 < 7.1999999999999996e-65

   1. Initial program 22.7%

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

   3. Taylor expanded in y1 around -inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. neg-mul-1 41.3%

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

      3. +-commutative 41.3%

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

      4. mul-1-neg 41.3%

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

      5. unsub-neg 41.3%

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

      6. *-commutative 41.3%

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

      7. *-commutative 41.3%

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

      8. *-commutative 41.3%

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

      9. *-commutative 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in i around -inf 59.5%

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

   if 7.1999999999999996e-65 < y4 < 1.1e171

   1. Initial program 32.7%

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

   3. Taylor expanded in b around inf 57.4%

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

   if 1.1e171 < y4

   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. Add Preprocessing

   3. Taylor expanded in t around inf 16.7%

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

      1. +-commutative 16.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 16.7%

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

      3. unsub-neg 16.7%

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

      4. *-commutative 16.7%

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

      5. *-commutative 16.7%

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

   5. Simplified 16.7%

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

   6. Taylor expanded in z around inf 50.9%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -7.5 \cdot 10^{+189}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;y4 \leq -2.45 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right) + \frac{y0 \cdot \left(c \cdot \left(x \cdot y2\right) - \left(b \cdot \left(x \cdot j\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}{z}\right)\\ \mathbf{elif}\;y4 \leq -1.7 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-143}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.8 \cdot 10^{-194}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.1 \cdot 10^{+171}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := y2 \cdot t\_3 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\\ \mathbf{if}\;y4 \leq -6.9 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot t\_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;k \cdot t\_4\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot t\_3 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;k \cdot \left(t\_4 + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.26 \cdot 10^{+171}:\\ \;\;\;\;t\_2 \cdot t\_3 + b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (+ (* y2 t_3) (* y (- (* i y5) (* b y4))))))
   (if (<= y4 -6.9e+149)
     (* y4 (+ (+ (* b t_1) (* y1 t_2)) (* c (- (* y y3) (* t y2)))))
     (if (<= y4 -5.7e+32)
       (* k t_4)
       (if (<= y4 -1e-120)
         (*
          y3
          (-
           (* y (- (* c y4) (* a y5)))
           (+ (* j t_3) (* z (- (* c y0) (* a y1))))))
         (if (<= y4 -2.2e-144)
           (* k (+ t_4 (* z (- (* b y0) (* i y1)))))
           (if (<= y4 1.3e-196)
             (*
              y5
              (+
               (* a (- (* t y2) (* y y3)))
               (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
             (if (<= y4 6.5e-65)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= y4 1.26e+171)
                 (+
                  (* t_2 t_3)
                  (*
                   b
                   (+
                    (+ (* a (- (* x y) (* z t))) (* y4 t_1))
                    (* y0 (- (* z k) (* x j))))))
                 (* t (* z (- (* c i) (* a b)))))))))))))

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 * j) - (y * k);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (y2 * t_3) + (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y4 <= -6.9e+149) {
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -5.7e+32) {
		tmp = k * t_4;
	} else if (y4 <= -1e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2.2e-144) {
		tmp = k * (t_4 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.3e-196) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 6.5e-65) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.26e+171) {
		tmp = (t_2 * t_3) + (b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j)))));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	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 = (t * j) - (y * k)
    t_2 = (k * y2) - (j * y3)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (y2 * t_3) + (y * ((i * y5) - (b * y4)))
    if (y4 <= (-6.9d+149)) then
        tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
    else if (y4 <= (-5.7d+32)) then
        tmp = k * t_4
    else if (y4 <= (-1d-120)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
    else if (y4 <= (-2.2d-144)) then
        tmp = k * (t_4 + (z * ((b * y0) - (i * y1))))
    else if (y4 <= 1.3d-196) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y4 <= 6.5d-65) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y4 <= 1.26d+171) then
        tmp = (t_2 * t_3) + (b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j)))))
    else
        tmp = t * (z * ((c * i) - (a * b)))
    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 * j) - (y * k);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (y2 * t_3) + (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y4 <= -6.9e+149) {
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -5.7e+32) {
		tmp = k * t_4;
	} else if (y4 <= -1e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2.2e-144) {
		tmp = k * (t_4 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 1.3e-196) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 6.5e-65) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.26e+171) {
		tmp = (t_2 * t_3) + (b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j)))));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (k * y2) - (j * y3)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (y2 * t_3) + (y * ((i * y5) - (b * y4)))
	tmp = 0
	if y4 <= -6.9e+149:
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
	elif y4 <= -5.7e+32:
		tmp = k * t_4
	elif y4 <= -1e-120:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))))
	elif y4 <= -2.2e-144:
		tmp = k * (t_4 + (z * ((b * y0) - (i * y1))))
	elif y4 <= 1.3e-196:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y4 <= 6.5e-65:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y4 <= 1.26e+171:
		tmp = (t_2 * t_3) + (b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j)))))
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	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 * j) - Float64(y * k))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(y2 * t_3) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	tmp = 0.0
	if (y4 <= -6.9e+149)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * t_2)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y4 <= -5.7e+32)
		tmp = Float64(k * t_4);
	elseif (y4 <= -1e-120)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(Float64(j * t_3) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y4 <= -2.2e-144)
		tmp = Float64(k * Float64(t_4 + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 1.3e-196)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y4 <= 6.5e-65)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y4 <= 1.26e+171)
		tmp = Float64(Float64(t_2 * t_3) + Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 * j) - (y * k);
	t_2 = (k * y2) - (j * y3);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (y2 * t_3) + (y * ((i * y5) - (b * y4)));
	tmp = 0.0;
	if (y4 <= -6.9e+149)
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	elseif (y4 <= -5.7e+32)
		tmp = k * t_4;
	elseif (y4 <= -1e-120)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) - ((j * t_3) + (z * ((c * y0) - (a * y1)))));
	elseif (y4 <= -2.2e-144)
		tmp = k * (t_4 + (z * ((b * y0) - (i * y1))));
	elseif (y4 <= 1.3e-196)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y4 <= 6.5e-65)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y4 <= 1.26e+171)
		tmp = (t_2 * t_3) + (b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j)))));
	else
		tmp = t * (z * ((c * i) - (a * b)));
	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 * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y2 * t$95$3), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.9e+149], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.7e+32], N[(k * t$95$4), $MachinePrecision], If[LessEqual[y4, -1e-120], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * t$95$3), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.2e-144], N[(k * N[(t$95$4 + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.3e-196], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e-65], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.26e+171], N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -6.9000000000000004e149

   1. Initial program 22.0%

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

   3. Taylor expanded in y4 around inf 58.7%

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

   if -6.9000000000000004e149 < y4 < -5.7e32

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 37.1%

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

      1. +-commutative 37.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 37.1%

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

      3. unsub-neg 37.1%

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

      4. *-commutative 37.1%

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

      5. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in k around inf 58.2%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -5.7e32 < y4 < -9.99999999999999979e-121

   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. Add Preprocessing

   3. Taylor expanded in y3 around -inf 63.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -9.99999999999999979e-121 < y4 < -2.20000000000000006e-144

   1. Initial program 38.1%

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

   3. Taylor expanded in k around inf 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -2.20000000000000006e-144 < y4 < 1.2999999999999999e-196

   1. Initial program 37.2%

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

   3. Taylor expanded in y5 around -inf 61.3%

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

   if 1.2999999999999999e-196 < y4 < 6.5e-65

   1. Initial program 22.7%

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

   3. Taylor expanded in y1 around -inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. neg-mul-1 41.3%

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

      3. +-commutative 41.3%

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

      4. mul-1-neg 41.3%

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

      5. unsub-neg 41.3%

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

      6. *-commutative 41.3%

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

      7. *-commutative 41.3%

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

      8. *-commutative 41.3%

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

      9. *-commutative 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in i around -inf 59.5%

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

   if 6.5e-65 < y4 < 1.26000000000000004e171

   1. Initial program 32.7%

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

   3. Taylor expanded in b around inf 57.4%

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

   if 1.26000000000000004e171 < y4

   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. Add Preprocessing

   3. Taylor expanded in t around inf 16.7%

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

      1. +-commutative 16.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 16.7%

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

      3. unsub-neg 16.7%

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

      4. *-commutative 16.7%

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

      5. *-commutative 16.7%

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

   5. Simplified 16.7%

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

   6. Taylor expanded in z around inf 50.9%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.9 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.26 \cdot 10^{+171}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y1 \cdot y4 - y0 \cdot y5\\ t_5 := y2 \cdot t\_4 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\\ t_6 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_1 + y1 \cdot t\_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;k \cdot t\_5\\ \mathbf{elif}\;y4 \leq -4.15 \cdot 10^{-122}:\\ \;\;\;\;y3 \cdot \left(y \cdot t\_6 - \left(j \cdot t\_4 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-145}:\\ \;\;\;\;k \cdot \left(t\_5 + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.8 \cdot 10^{-198}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_2 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.4 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+171}:\\ \;\;\;\;t\_3 \cdot t\_4 + \left(b \cdot \left(y4 \cdot t\_1\right) - t\_2 \cdot t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (- (* y1 y4) (* y0 y5)))
        (t_5 (+ (* y2 t_4) (* y (- (* i y5) (* b y4)))))
        (t_6 (- (* c y4) (* a y5))))
   (if (<= y4 -1.25e+150)
     (* y4 (+ (+ (* b t_1) (* y1 t_3)) (* c (- (* y y3) (* t y2)))))
     (if (<= y4 -5.9e+32)
       (* k t_5)
       (if (<= y4 -4.15e-122)
         (* y3 (- (* y t_6) (+ (* j t_4) (* z (- (* c y0) (* a y1))))))
         (if (<= y4 -2.2e-145)
           (* k (+ t_5 (* z (- (* b y0) (* i y1)))))
           (if (<= y4 2.8e-198)
             (*
              y5
              (+
               (* a t_2)
               (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
             (if (<= y4 9.4e-58)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= y4 1.35e+171)
                 (+ (* t_3 t_4) (- (* b (* y4 t_1)) (* t_2 t_6)))
                 (* t (* z (- (* c i) (* a b)))))))))))))

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 * j) - (y * k);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = (y2 * t_4) + (y * ((i * y5) - (b * y4)));
	double t_6 = (c * y4) - (a * y5);
	double tmp;
	if (y4 <= -1.25e+150) {
		tmp = y4 * (((b * t_1) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -5.9e+32) {
		tmp = k * t_5;
	} else if (y4 <= -4.15e-122) {
		tmp = y3 * ((y * t_6) - ((j * t_4) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2.2e-145) {
		tmp = k * (t_5 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 2.8e-198) {
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 9.4e-58) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.35e+171) {
		tmp = (t_3 * t_4) + ((b * (y4 * t_1)) - (t_2 * t_6));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	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 = (t * j) - (y * k)
    t_2 = (t * y2) - (y * y3)
    t_3 = (k * y2) - (j * y3)
    t_4 = (y1 * y4) - (y0 * y5)
    t_5 = (y2 * t_4) + (y * ((i * y5) - (b * y4)))
    t_6 = (c * y4) - (a * y5)
    if (y4 <= (-1.25d+150)) then
        tmp = y4 * (((b * t_1) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (y4 <= (-5.9d+32)) then
        tmp = k * t_5
    else if (y4 <= (-4.15d-122)) then
        tmp = y3 * ((y * t_6) - ((j * t_4) + (z * ((c * y0) - (a * y1)))))
    else if (y4 <= (-2.2d-145)) then
        tmp = k * (t_5 + (z * ((b * y0) - (i * y1))))
    else if (y4 <= 2.8d-198) then
        tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y4 <= 9.4d-58) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y4 <= 1.35d+171) then
        tmp = (t_3 * t_4) + ((b * (y4 * t_1)) - (t_2 * t_6))
    else
        tmp = t * (z * ((c * i) - (a * b)))
    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 * j) - (y * k);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (y1 * y4) - (y0 * y5);
	double t_5 = (y2 * t_4) + (y * ((i * y5) - (b * y4)));
	double t_6 = (c * y4) - (a * y5);
	double tmp;
	if (y4 <= -1.25e+150) {
		tmp = y4 * (((b * t_1) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (y4 <= -5.9e+32) {
		tmp = k * t_5;
	} else if (y4 <= -4.15e-122) {
		tmp = y3 * ((y * t_6) - ((j * t_4) + (z * ((c * y0) - (a * y1)))));
	} else if (y4 <= -2.2e-145) {
		tmp = k * (t_5 + (z * ((b * y0) - (i * y1))));
	} else if (y4 <= 2.8e-198) {
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y4 <= 9.4e-58) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y4 <= 1.35e+171) {
		tmp = (t_3 * t_4) + ((b * (y4 * t_1)) - (t_2 * t_6));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (t * y2) - (y * y3)
	t_3 = (k * y2) - (j * y3)
	t_4 = (y1 * y4) - (y0 * y5)
	t_5 = (y2 * t_4) + (y * ((i * y5) - (b * y4)))
	t_6 = (c * y4) - (a * y5)
	tmp = 0
	if y4 <= -1.25e+150:
		tmp = y4 * (((b * t_1) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	elif y4 <= -5.9e+32:
		tmp = k * t_5
	elif y4 <= -4.15e-122:
		tmp = y3 * ((y * t_6) - ((j * t_4) + (z * ((c * y0) - (a * y1)))))
	elif y4 <= -2.2e-145:
		tmp = k * (t_5 + (z * ((b * y0) - (i * y1))))
	elif y4 <= 2.8e-198:
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y4 <= 9.4e-58:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y4 <= 1.35e+171:
		tmp = (t_3 * t_4) + ((b * (y4 * t_1)) - (t_2 * t_6))
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	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 * j) - Float64(y * k))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_5 = Float64(Float64(y2 * t_4) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	t_6 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (y4 <= -1.25e+150)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y4 <= -5.9e+32)
		tmp = Float64(k * t_5);
	elseif (y4 <= -4.15e-122)
		tmp = Float64(y3 * Float64(Float64(y * t_6) - Float64(Float64(j * t_4) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y4 <= -2.2e-145)
		tmp = Float64(k * Float64(t_5 + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y4 <= 2.8e-198)
		tmp = Float64(y5 * Float64(Float64(a * t_2) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y4 <= 9.4e-58)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y4 <= 1.35e+171)
		tmp = Float64(Float64(t_3 * t_4) + Float64(Float64(b * Float64(y4 * t_1)) - Float64(t_2 * t_6)));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 * j) - (y * k);
	t_2 = (t * y2) - (y * y3);
	t_3 = (k * y2) - (j * y3);
	t_4 = (y1 * y4) - (y0 * y5);
	t_5 = (y2 * t_4) + (y * ((i * y5) - (b * y4)));
	t_6 = (c * y4) - (a * y5);
	tmp = 0.0;
	if (y4 <= -1.25e+150)
		tmp = y4 * (((b * t_1) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (y4 <= -5.9e+32)
		tmp = k * t_5;
	elseif (y4 <= -4.15e-122)
		tmp = y3 * ((y * t_6) - ((j * t_4) + (z * ((c * y0) - (a * y1)))));
	elseif (y4 <= -2.2e-145)
		tmp = k * (t_5 + (z * ((b * y0) - (i * y1))));
	elseif (y4 <= 2.8e-198)
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y4 <= 9.4e-58)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y4 <= 1.35e+171)
		tmp = (t_3 * t_4) + ((b * (y4 * t_1)) - (t_2 * t_6));
	else
		tmp = t * (z * ((c * i) - (a * b)));
	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 * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y2 * t$95$4), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.25e+150], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.9e+32], N[(k * t$95$5), $MachinePrecision], If[LessEqual[y4, -4.15e-122], N[(y3 * N[(N[(y * t$95$6), $MachinePrecision] - N[(N[(j * t$95$4), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.2e-145], N[(k * N[(t$95$5 + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.8e-198], N[(y5 * N[(N[(a * t$95$2), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.4e-58], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.35e+171], N[(N[(t$95$3 * t$95$4), $MachinePrecision] + N[(N[(b * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -1.25000000000000002e150

   1. Initial program 22.0%

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

   3. Taylor expanded in y4 around inf 58.7%

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

   if -1.25000000000000002e150 < y4 < -5.89999999999999965e32

   1. Initial program 31.6%

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

   3. Taylor expanded in y around inf 37.1%

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

      1. +-commutative 37.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 37.1%

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

      3. unsub-neg 37.1%

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

      4. *-commutative 37.1%

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

      5. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in k around inf 58.2%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -5.89999999999999965e32 < y4 < -4.1500000000000002e-122

   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. Add Preprocessing

   3. Taylor expanded in y3 around -inf 63.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -4.1500000000000002e-122 < y4 < -2.19999999999999999e-145

   1. Initial program 38.1%

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

   3. Taylor expanded in k around inf 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 75.4%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 75.4%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -2.19999999999999999e-145 < y4 < 2.7999999999999999e-198

   1. Initial program 37.2%

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

   3. Taylor expanded in y5 around -inf 61.3%

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

   if 2.7999999999999999e-198 < y4 < 9.39999999999999989e-58

   1. Initial program 20.8%

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

   3. Taylor expanded in y1 around -inf 42.0%

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

      1. associate-*r* 42.0%

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

      2. neg-mul-1 42.0%

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

      3. +-commutative 42.0%

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

      4. mul-1-neg 42.0%

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

      5. unsub-neg 42.0%

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

      6. *-commutative 42.0%

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

      7. *-commutative 42.0%

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

      8. *-commutative 42.0%

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

      9. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in i around -inf 58.7%

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

   if 9.39999999999999989e-58 < y4 < 1.3499999999999999e171

   1. Initial program 34.1%

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

   3. Taylor expanded in y4 around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 1.3499999999999999e171 < y4

   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. Add Preprocessing

   3. Taylor expanded in t around inf 16.7%

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

      1. +-commutative 16.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 16.7%

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

      3. unsub-neg 16.7%

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

      4. *-commutative 16.7%

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

      5. *-commutative 16.7%

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

   5. Simplified 16.7%

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

   6. Taylor expanded in z around inf 50.9%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.15 \cdot 10^{-122}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-145}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.8 \cdot 10^{-198}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.4 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{+171}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-20}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y3 (+ (* j (- (* y0 y5) (* y1 y4))) (* y (- (* c y4) (* a y5))))))
        (t_2 (* j (* b (- (* t y4) (* x y0))))))
   (if (<= b -2.1e+116)
     t_2
     (if (<= b -1.25e-56)
       t_1
       (if (<= b -6e-104)
         (* a (* t (* y2 y5)))
         (if (<= b -1.6e-115)
           t_1
           (if (<= b -3.45e-231)
             (* i (* y1 (- (* x j) (* z k))))
             (if (<= b -5.8e-263)
               (* y1 (* y4 (- (* k y2) (* j y3))))
               (if (<= b -3.6e-301)
                 (* (* t c) (- (* z i) (* y2 y4)))
                 (if (<= b 7e-233)
                   (* y1 (* z (- (* a y3) (* i k))))
                   (if (<= b 1.55e-127)
                     (* b (* x (- (* y a) (* j y0))))
                     (if (<= b 1.6e-20)
                       (*
                        k
                        (+
                         (* y2 (- (* y1 y4) (* y0 y5)))
                         (* y (- (* i y5) (* b y4)))))
                       (if (<= b 3.7e+111)
                         t_1
                         (if (<= b 1.08e+231)
                           (* t (* z (- (* c i) (* a b))))
                           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 = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * ((c * y4) - (a * y5))));
	double t_2 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -2.1e+116) {
		tmp = t_2;
	} else if (b <= -1.25e-56) {
		tmp = t_1;
	} else if (b <= -6e-104) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -1.6e-115) {
		tmp = t_1;
	} else if (b <= -3.45e-231) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= -5.8e-263) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= -3.6e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 7e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.55e-127) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.6e-20) {
		tmp = k * ((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4))));
	} else if (b <= 3.7e+111) {
		tmp = t_1;
	} else if (b <= 1.08e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * ((c * y4) - (a * y5))))
    t_2 = j * (b * ((t * y4) - (x * y0)))
    if (b <= (-2.1d+116)) then
        tmp = t_2
    else if (b <= (-1.25d-56)) then
        tmp = t_1
    else if (b <= (-6d-104)) then
        tmp = a * (t * (y2 * y5))
    else if (b <= (-1.6d-115)) then
        tmp = t_1
    else if (b <= (-3.45d-231)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (b <= (-5.8d-263)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (b <= (-3.6d-301)) then
        tmp = (t * c) * ((z * i) - (y2 * y4))
    else if (b <= 7d-233) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 1.55d-127) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 1.6d-20) then
        tmp = k * ((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4))))
    else if (b <= 3.7d+111) then
        tmp = t_1
    else if (b <= 1.08d+231) then
        tmp = t * (z * ((c * i) - (a * b)))
    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 = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * ((c * y4) - (a * y5))));
	double t_2 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -2.1e+116) {
		tmp = t_2;
	} else if (b <= -1.25e-56) {
		tmp = t_1;
	} else if (b <= -6e-104) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -1.6e-115) {
		tmp = t_1;
	} else if (b <= -3.45e-231) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= -5.8e-263) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= -3.6e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 7e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 1.55e-127) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.6e-20) {
		tmp = k * ((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4))));
	} else if (b <= 3.7e+111) {
		tmp = t_1;
	} else if (b <= 1.08e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * ((c * y4) - (a * y5))))
	t_2 = j * (b * ((t * y4) - (x * y0)))
	tmp = 0
	if b <= -2.1e+116:
		tmp = t_2
	elif b <= -1.25e-56:
		tmp = t_1
	elif b <= -6e-104:
		tmp = a * (t * (y2 * y5))
	elif b <= -1.6e-115:
		tmp = t_1
	elif b <= -3.45e-231:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif b <= -5.8e-263:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif b <= -3.6e-301:
		tmp = (t * c) * ((z * i) - (y2 * y4))
	elif b <= 7e-233:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 1.55e-127:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 1.6e-20:
		tmp = k * ((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4))))
	elif b <= 3.7e+111:
		tmp = t_1
	elif b <= 1.08e+231:
		tmp = t * (z * ((c * i) - (a * b)))
	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(y3 * Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))))
	t_2 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -2.1e+116)
		tmp = t_2;
	elseif (b <= -1.25e-56)
		tmp = t_1;
	elseif (b <= -6e-104)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (b <= -1.6e-115)
		tmp = t_1;
	elseif (b <= -3.45e-231)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (b <= -5.8e-263)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (b <= -3.6e-301)
		tmp = Float64(Float64(t * c) * Float64(Float64(z * i) - Float64(y2 * y4)));
	elseif (b <= 7e-233)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 1.55e-127)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 1.6e-20)
		tmp = Float64(k * Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))));
	elseif (b <= 3.7e+111)
		tmp = t_1;
	elseif (b <= 1.08e+231)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * ((c * y4) - (a * y5))));
	t_2 = j * (b * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (b <= -2.1e+116)
		tmp = t_2;
	elseif (b <= -1.25e-56)
		tmp = t_1;
	elseif (b <= -6e-104)
		tmp = a * (t * (y2 * y5));
	elseif (b <= -1.6e-115)
		tmp = t_1;
	elseif (b <= -3.45e-231)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (b <= -5.8e-263)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (b <= -3.6e-301)
		tmp = (t * c) * ((z * i) - (y2 * y4));
	elseif (b <= 7e-233)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 1.55e-127)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 1.6e-20)
		tmp = k * ((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4))));
	elseif (b <= 3.7e+111)
		tmp = t_1;
	elseif (b <= 1.08e+231)
		tmp = t * (z * ((c * i) - (a * b)));
	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[(y3 * N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+116], t$95$2, If[LessEqual[b, -1.25e-56], t$95$1, If[LessEqual[b, -6e-104], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-115], t$95$1, If[LessEqual[b, -3.45e-231], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-263], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-301], N[(N[(t * c), $MachinePrecision] * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-233], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-127], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-20], N[(k * N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+111], t$95$1, If[LessEqual[b, 1.08e+231], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if b < -2.1000000000000001e116 or 1.08000000000000001e231 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 45.5%

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

      1. +-commutative 45.5%

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

      2. mul-1-neg 45.5%

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

      3. unsub-neg 45.5%

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

      4. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in b around inf 63.9%

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

   if -2.1000000000000001e116 < b < -1.24999999999999999e-56 or -6.0000000000000005e-104 < b < -1.6e-115 or 1.59999999999999985e-20 < b < 3.7000000000000003e111

   1. Initial program 31.5%

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

   3. Taylor expanded in y around inf 38.8%

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

      1. +-commutative 38.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 38.8%

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

      3. unsub-neg 38.8%

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

      4. *-commutative 38.8%

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

      5. *-commutative 38.8%

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

   5. Simplified 38.8%

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

   6. Taylor expanded in y3 around -inf 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -1.24999999999999999e-56 < b < -6.0000000000000005e-104

   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. Add Preprocessing

   3. Taylor expanded in y around inf 45.6%

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

      1. +-commutative 45.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in y around 0 45.6%

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

   7. Taylor expanded in a around inf 73.2%

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

      1. *-commutative 73.2%

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

   9. Simplified 73.2%

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

   if -1.6e-115 < b < -3.45000000000000001e-231

   1. Initial program 23.2%

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

   3. Taylor expanded in y1 around -inf 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

      3. +-commutative 47.4%

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

      4. mul-1-neg 47.4%

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

      5. unsub-neg 47.4%

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

      6. *-commutative 47.4%

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

      7. *-commutative 47.4%

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

      8. *-commutative 47.4%

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

      9. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in i around -inf 47.3%

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

   if -3.45000000000000001e-231 < b < -5.80000000000000007e-263

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.3%

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

      1. associate-*r* 43.3%

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

      2. neg-mul-1 43.3%

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

      3. +-commutative 43.3%

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

      4. mul-1-neg 43.3%

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

      5. unsub-neg 43.3%

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

      6. *-commutative 43.3%

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

      7. *-commutative 43.3%

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

      8. *-commutative 43.3%

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

      9. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in y4 around -inf 72.0%

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

   if -5.80000000000000007e-263 < b < -3.60000000000000007e-301

   1. Initial program 64.3%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. +-commutative 64.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in c around -inf 47.6%

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

      1. associate-*r* 47.6%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)} \]

      2. *-commutative 47.6%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \]

      3. +-commutative 47.6%

         \[\leadsto \left(t \cdot c\right) \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \]

      4. mul-1-neg 47.6%

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

      5. unsub-neg 47.6%

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

   8. Simplified 47.6%

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

   if -3.60000000000000007e-301 < b < 6.99999999999999982e-233

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 54.6%

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

      1. associate-*r* 54.6%

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

      2. neg-mul-1 54.6%

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

      3. +-commutative 54.6%

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

      4. mul-1-neg 54.6%

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

      5. unsub-neg 54.6%

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

      6. *-commutative 54.6%

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

      7. *-commutative 54.6%

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

      8. *-commutative 54.6%

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

      9. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in z around -inf 72.7%

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

   if 6.99999999999999982e-233 < b < 1.55e-127

   1. Initial program 28.4%

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

   3. Taylor expanded in b around inf 28.6%

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

   4. Taylor expanded in x around inf 44.7%

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

   if 1.55e-127 < b < 1.59999999999999985e-20

   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. Add Preprocessing

   3. Taylor expanded in y around inf 56.5%

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

      1. +-commutative 56.5%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

      5. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in k around inf 61.1%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 3.7000000000000003e111 < b < 1.08000000000000001e231

   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. Add Preprocessing

   3. Taylor expanded in t around inf 34.5%

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

      1. +-commutative 34.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.5%

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

      3. unsub-neg 34.5%

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

      4. *-commutative 34.5%

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

      5. *-commutative 34.5%

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

   5. Simplified 34.5%

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

   6. Taylor expanded in z around inf 52.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-56}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-115}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-20}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_3 := y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k\right)\right) + t\_2\right)\\ t_4 := t \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_5 := j \cdot \left(\left(t\_4 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -7.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq -1.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot t\_4\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-297}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq 1.92 \cdot 10^{-78}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(t\_2 - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
           (* b (- (* z k) (* x j))))))
        (t_2 (* c (- (* y y3) (* t y2))))
        (t_3 (* y4 (+ (- (* y1 (- (* k y2) (* j y3))) (* b (* y k))) t_2)))
        (t_4 (* t (- (* b y4) (* i y5))))
        (t_5
         (*
          j
          (+
           (+ t_4 (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= y0 -7.5e+56)
     t_1
     (if (<= y0 -1.45e-67)
       (*
        y2
        (-
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t (- (* c y4) (* a y5)))))
       (if (<= y0 -1.02e-106)
         t_3
         (if (<= y0 -1.9e-185)
           (* j t_4)
           (if (<= y0 -8e-282)
             (* t (* z (- (* c i) (* a b))))
             (if (<= y0 -3e-297)
               t_5
               (if (<= y0 4.5e-204)
                 t_3
                 (if (<= y0 1.92e-78)
                   t_5
                   (if (<= y0 6.5e+98)
                     (* y4 (- t_2 (* j (* y1 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 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_2 = c * ((y * y3) - (t * y2));
	double t_3 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * (y * k))) + t_2);
	double t_4 = t * ((b * y4) - (i * y5));
	double t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y0 <= -7.5e+56) {
		tmp = t_1;
	} else if (y0 <= -1.45e-67) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (y0 <= -1.02e-106) {
		tmp = t_3;
	} else if (y0 <= -1.9e-185) {
		tmp = j * t_4;
	} else if (y0 <= -8e-282) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= -3e-297) {
		tmp = t_5;
	} else if (y0 <= 4.5e-204) {
		tmp = t_3;
	} else if (y0 <= 1.92e-78) {
		tmp = t_5;
	} else if (y0 <= 6.5e+98) {
		tmp = y4 * (t_2 - (j * (y1 * 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    t_2 = c * ((y * y3) - (t * y2))
    t_3 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * (y * k))) + t_2)
    t_4 = t * ((b * y4) - (i * y5))
    t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    if (y0 <= (-7.5d+56)) then
        tmp = t_1
    else if (y0 <= (-1.45d-67)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))))
    else if (y0 <= (-1.02d-106)) then
        tmp = t_3
    else if (y0 <= (-1.9d-185)) then
        tmp = j * t_4
    else if (y0 <= (-8d-282)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y0 <= (-3d-297)) then
        tmp = t_5
    else if (y0 <= 4.5d-204) then
        tmp = t_3
    else if (y0 <= 1.92d-78) then
        tmp = t_5
    else if (y0 <= 6.5d+98) then
        tmp = y4 * (t_2 - (j * (y1 * 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 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_2 = c * ((y * y3) - (t * y2));
	double t_3 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * (y * k))) + t_2);
	double t_4 = t * ((b * y4) - (i * y5));
	double t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y0 <= -7.5e+56) {
		tmp = t_1;
	} else if (y0 <= -1.45e-67) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (y0 <= -1.02e-106) {
		tmp = t_3;
	} else if (y0 <= -1.9e-185) {
		tmp = j * t_4;
	} else if (y0 <= -8e-282) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= -3e-297) {
		tmp = t_5;
	} else if (y0 <= 4.5e-204) {
		tmp = t_3;
	} else if (y0 <= 1.92e-78) {
		tmp = t_5;
	} else if (y0 <= 6.5e+98) {
		tmp = y4 * (t_2 - (j * (y1 * 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 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	t_2 = c * ((y * y3) - (t * y2))
	t_3 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * (y * k))) + t_2)
	t_4 = t * ((b * y4) - (i * y5))
	t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if y0 <= -7.5e+56:
		tmp = t_1
	elif y0 <= -1.45e-67:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))))
	elif y0 <= -1.02e-106:
		tmp = t_3
	elif y0 <= -1.9e-185:
		tmp = j * t_4
	elif y0 <= -8e-282:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y0 <= -3e-297:
		tmp = t_5
	elif y0 <= 4.5e-204:
		tmp = t_3
	elif y0 <= 1.92e-78:
		tmp = t_5
	elif y0 <= 6.5e+98:
		tmp = y4 * (t_2 - (j * (y1 * 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(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	t_3 = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(b * Float64(y * k))) + t_2))
	t_4 = Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))
	t_5 = Float64(j * Float64(Float64(t_4 + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y0 <= -7.5e+56)
		tmp = t_1;
	elseif (y0 <= -1.45e-67)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y0 <= -1.02e-106)
		tmp = t_3;
	elseif (y0 <= -1.9e-185)
		tmp = Float64(j * t_4);
	elseif (y0 <= -8e-282)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y0 <= -3e-297)
		tmp = t_5;
	elseif (y0 <= 4.5e-204)
		tmp = t_3;
	elseif (y0 <= 1.92e-78)
		tmp = t_5;
	elseif (y0 <= 6.5e+98)
		tmp = Float64(y4 * Float64(t_2 - Float64(j * Float64(y1 * 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 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	t_2 = c * ((y * y3) - (t * y2));
	t_3 = y4 * (((y1 * ((k * y2) - (j * y3))) - (b * (y * k))) + t_2);
	t_4 = t * ((b * y4) - (i * y5));
	t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y0 <= -7.5e+56)
		tmp = t_1;
	elseif (y0 <= -1.45e-67)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	elseif (y0 <= -1.02e-106)
		tmp = t_3;
	elseif (y0 <= -1.9e-185)
		tmp = j * t_4;
	elseif (y0 <= -8e-282)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y0 <= -3e-297)
		tmp = t_5;
	elseif (y0 <= 4.5e-204)
		tmp = t_3;
	elseif (y0 <= 1.92e-78)
		tmp = t_5;
	elseif (y0 <= 6.5e+98)
		tmp = y4 * (t_2 - (j * (y1 * 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[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(j * N[(N[(t$95$4 + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7.5e+56], t$95$1, If[LessEqual[y0, -1.45e-67], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.02e-106], t$95$3, If[LessEqual[y0, -1.9e-185], N[(j * t$95$4), $MachinePrecision], If[LessEqual[y0, -8e-282], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3e-297], t$95$5, If[LessEqual[y0, 4.5e-204], t$95$3, If[LessEqual[y0, 1.92e-78], t$95$5, If[LessEqual[y0, 6.5e+98], N[(y4 * N[(t$95$2 - N[(j * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -7.4999999999999999e56 or 6.4999999999999999e98 < y0

   1. Initial program 23.0%

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

   3. Taylor expanded in y0 around inf 57.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 57.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 57.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 57.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 57.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   if -7.4999999999999999e56 < y0 < -1.45000000000000002e-67

   1. Initial program 33.2%

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

   3. Taylor expanded in y2 around inf 52.5%

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

   if -1.45000000000000002e-67 < y0 < -1.02e-106 or -2.99999999999999995e-297 < y0 < 4.49999999999999974e-204

   1. Initial program 44.4%

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

   3. Taylor expanded in y around inf 44.7%

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

      1. +-commutative 44.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

      4. *-commutative 44.7%

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

      5. *-commutative 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in y4 around inf 61.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.02e-106 < y0 < -1.9e-185

   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. Add Preprocessing

   3. Taylor expanded in j around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in t around inf 65.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -1.9e-185 < y0 < -8.0000000000000001e-282

   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. Add Preprocessing

   3. Taylor expanded in t around inf 47.5%

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

      1. +-commutative 47.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

      5. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -8.0000000000000001e-282 < y0 < -2.99999999999999995e-297 or 4.49999999999999974e-204 < y0 < 1.92000000000000005e-78

   1. Initial program 35.4%

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

   3. Taylor expanded in j around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

      4. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if 1.92000000000000005e-78 < y0 < 6.4999999999999999e98

   1. Initial program 24.9%

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

   3. Taylor expanded in y around inf 32.0%

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

      1. +-commutative 32.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 32.0%

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

      3. unsub-neg 32.0%

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

      4. *-commutative 32.0%

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

      5. *-commutative 32.0%

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

   5. Simplified 32.0%

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

   6. Taylor expanded in k around 0 21.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 46.7%

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

      1. associate-*r* 46.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 46.7%

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

      3. *-commutative 46.7%

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

   9. Simplified 46.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.5 \cdot 10^{+56}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -8 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.92 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right) - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := x \cdot \left(i \cdot y1 - b \cdot y0\right)\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y0 \cdot y5 - y1 \cdot y4\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := y \cdot t\_1\\ \mathbf{if}\;y3 \leq -7.4 \cdot 10^{+132}:\\ \;\;\;\;y3 \cdot \left(j \cdot t\_4 + t\_6\right)\\ \mathbf{elif}\;y3 \leq -1.2 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq -4.7 \cdot 10^{-18}:\\ \;\;\;\;t\_3 \cdot t\_5 - t \cdot \left(y2 \cdot t\_1\right)\\ \mathbf{elif}\;y3 \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;j \cdot t\_2\\ \mathbf{elif}\;y3 \leq -1.4 \cdot 10^{-275}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_5 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_3\right)\\ \mathbf{elif}\;y3 \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot t\_4\right) + t\_2\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{+43}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t\_3 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(t\_6 - \left(j \cdot t\_5 + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (* x (- (* i y1) (* b y0))))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (- (* y0 y5) (* y1 y4)))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* y t_1)))
   (if (<= y3 -7.4e+132)
     (* y3 (+ (* j t_4) t_6))
     (if (<= y3 -1.2e+74)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= y3 -4.7e-18)
         (- (* t_3 t_5) (* t (* y2 t_1)))
         (if (<= y3 -2.4e-88)
           (* j t_2)
           (if (<= y3 -1.4e-275)
             (*
              k
              (+
               (+ (* y2 t_5) (* y (- (* i y5) (* b y4))))
               (* z (- (* b y0) (* i y1)))))
             (if (<= y3 4.5e-266)
               (* y0 (* y2 (- (* x c) (* k y5))))
               (if (<= y3 2.1e-199)
                 (* y4 (+ (* b (- (* t j) (* y k))) (* y1 t_3)))
                 (if (<= y3 4.1e-81)
                   (* j (+ (+ (* t (- (* b y4) (* i y5))) (* y3 t_4)) t_2))
                   (if (<= y3 2.9e+43)
                     (*
                      y1
                      (+
                       (* i (- (* x j) (* z k)))
                       (+ (* y4 t_3) (* a (- (* z y3) (* x y2))))))
                     (*
                      y3
                      (-
                       t_6
                       (+ (* j t_5) (* z (- (* c y0) (* a y1)))))))))))))))))

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 * y4) - (a * y5);
	double t_2 = x * ((i * y1) - (b * y0));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y * t_1;
	double tmp;
	if (y3 <= -7.4e+132) {
		tmp = y3 * ((j * t_4) + t_6);
	} else if (y3 <= -1.2e+74) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y3 <= -4.7e-18) {
		tmp = (t_3 * t_5) - (t * (y2 * t_1));
	} else if (y3 <= -2.4e-88) {
		tmp = j * t_2;
	} else if (y3 <= -1.4e-275) {
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y3 <= 4.5e-266) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y3 <= 2.1e-199) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (y1 * t_3));
	} else if (y3 <= 4.1e-81) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_4)) + t_2);
	} else if (y3 <= 2.9e+43) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else {
		tmp = y3 * (t_6 - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	}
	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 = (c * y4) - (a * y5)
    t_2 = x * ((i * y1) - (b * y0))
    t_3 = (k * y2) - (j * y3)
    t_4 = (y0 * y5) - (y1 * y4)
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = y * t_1
    if (y3 <= (-7.4d+132)) then
        tmp = y3 * ((j * t_4) + t_6)
    else if (y3 <= (-1.2d+74)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y3 <= (-4.7d-18)) then
        tmp = (t_3 * t_5) - (t * (y2 * t_1))
    else if (y3 <= (-2.4d-88)) then
        tmp = j * t_2
    else if (y3 <= (-1.4d-275)) then
        tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (y3 <= 4.5d-266) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (y3 <= 2.1d-199) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + (y1 * t_3))
    else if (y3 <= 4.1d-81) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_4)) + t_2)
    else if (y3 <= 2.9d+43) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
    else
        tmp = y3 * (t_6 - ((j * t_5) + (z * ((c * y0) - (a * y1)))))
    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 * y4) - (a * y5);
	double t_2 = x * ((i * y1) - (b * y0));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y * t_1;
	double tmp;
	if (y3 <= -7.4e+132) {
		tmp = y3 * ((j * t_4) + t_6);
	} else if (y3 <= -1.2e+74) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y3 <= -4.7e-18) {
		tmp = (t_3 * t_5) - (t * (y2 * t_1));
	} else if (y3 <= -2.4e-88) {
		tmp = j * t_2;
	} else if (y3 <= -1.4e-275) {
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y3 <= 4.5e-266) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y3 <= 2.1e-199) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + (y1 * t_3));
	} else if (y3 <= 4.1e-81) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_4)) + t_2);
	} else if (y3 <= 2.9e+43) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else {
		tmp = y3 * (t_6 - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	t_2 = x * ((i * y1) - (b * y0))
	t_3 = (k * y2) - (j * y3)
	t_4 = (y0 * y5) - (y1 * y4)
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = y * t_1
	tmp = 0
	if y3 <= -7.4e+132:
		tmp = y3 * ((j * t_4) + t_6)
	elif y3 <= -1.2e+74:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y3 <= -4.7e-18:
		tmp = (t_3 * t_5) - (t * (y2 * t_1))
	elif y3 <= -2.4e-88:
		tmp = j * t_2
	elif y3 <= -1.4e-275:
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif y3 <= 4.5e-266:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif y3 <= 2.1e-199:
		tmp = y4 * ((b * ((t * j) - (y * k))) + (y1 * t_3))
	elif y3 <= 4.1e-81:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_4)) + t_2)
	elif y3 <= 2.9e+43:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
	else:
		tmp = y3 * (t_6 - ((j * t_5) + (z * ((c * y0) - (a * y1)))))
	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(c * y4) - Float64(a * y5))
	t_2 = Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(y * t_1)
	tmp = 0.0
	if (y3 <= -7.4e+132)
		tmp = Float64(y3 * Float64(Float64(j * t_4) + t_6));
	elseif (y3 <= -1.2e+74)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y3 <= -4.7e-18)
		tmp = Float64(Float64(t_3 * t_5) - Float64(t * Float64(y2 * t_1)));
	elseif (y3 <= -2.4e-88)
		tmp = Float64(j * t_2);
	elseif (y3 <= -1.4e-275)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_5) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y3 <= 4.5e-266)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (y3 <= 2.1e-199)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_3)));
	elseif (y3 <= 4.1e-81)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * t_4)) + t_2));
	elseif (y3 <= 2.9e+43)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_3) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	else
		tmp = Float64(y3 * Float64(t_6 - Float64(Float64(j * t_5) + Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	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 * y4) - (a * y5);
	t_2 = x * ((i * y1) - (b * y0));
	t_3 = (k * y2) - (j * y3);
	t_4 = (y0 * y5) - (y1 * y4);
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = y * t_1;
	tmp = 0.0;
	if (y3 <= -7.4e+132)
		tmp = y3 * ((j * t_4) + t_6);
	elseif (y3 <= -1.2e+74)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y3 <= -4.7e-18)
		tmp = (t_3 * t_5) - (t * (y2 * t_1));
	elseif (y3 <= -2.4e-88)
		tmp = j * t_2;
	elseif (y3 <= -1.4e-275)
		tmp = k * (((y2 * t_5) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (y3 <= 4.5e-266)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (y3 <= 2.1e-199)
		tmp = y4 * ((b * ((t * j) - (y * k))) + (y1 * t_3));
	elseif (y3 <= 4.1e-81)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_4)) + t_2);
	elseif (y3 <= 2.9e+43)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	else
		tmp = y3 * (t_6 - ((j * t_5) + (z * ((c * y0) - (a * y1)))));
	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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[y3, -7.4e+132], N[(y3 * N[(N[(j * t$95$4), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.2e+74], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.7e-18], N[(N[(t$95$3 * t$95$5), $MachinePrecision] - N[(t * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.4e-88], N[(j * t$95$2), $MachinePrecision], If[LessEqual[y3, -1.4e-275], N[(k * N[(N[(N[(y2 * t$95$5), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e-266], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e-199], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.1e-81], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.9e+43], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$3), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(t$95$6 - N[(N[(j * t$95$5), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y3 < -7.40000000000000022e132

   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. Add Preprocessing

   3. Taylor expanded in y around inf 34.3%

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

      1. +-commutative 34.3%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.3%

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

      3. unsub-neg 34.3%

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

      4. *-commutative 34.3%

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

      5. *-commutative 34.3%

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

   5. Simplified 34.3%

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

   6. Taylor expanded in y3 around -inf 63.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if -7.40000000000000022e132 < y3 < -1.20000000000000004e74

   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. Add Preprocessing

   3. Taylor expanded in b around inf 27.3%

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

   4. Taylor expanded in z around -inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. neg-mul-1 61.2%

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

   6. Simplified 61.2%

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

   if -1.20000000000000004e74 < y3 < -4.6999999999999996e-18

   1. Initial program 37.4%

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

   3. Taylor expanded in y around inf 43.9%

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

      1. +-commutative 43.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 43.9%

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

      3. unsub-neg 43.9%

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

      4. *-commutative 43.9%

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

      5. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in y around 0 68.9%

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

   if -4.6999999999999996e-18 < y3 < -2.4e-88

   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. Add Preprocessing

   3. Taylor expanded in j around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

      4. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in x around inf 57.0%

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

   if -2.4e-88 < y3 < -1.39999999999999997e-275

   1. Initial program 40.8%

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

   3. Taylor expanded in k around inf 50.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -1.39999999999999997e-275 < y3 < 4.5000000000000003e-266

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 53.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 53.2%

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

      3. unsub-neg 53.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 53.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 53.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 53.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 53.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 63.9%

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

   if 4.5000000000000003e-266 < y3 < 2.10000000000000002e-199

   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. Add Preprocessing

   3. Taylor expanded in b around inf 58.3%

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

   4. Taylor expanded in y4 around inf 83.7%

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

   if 2.10000000000000002e-199 < y3 < 4.09999999999999984e-81

   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. Add Preprocessing

   3. Taylor expanded in j around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   if 4.09999999999999984e-81 < y3 < 2.9000000000000002e43

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 58.9%

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

      1. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. +-commutative 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. *-commutative 58.9%

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

      7. *-commutative 58.9%

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

      8. *-commutative 58.9%

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

      9. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   if 2.9000000000000002e43 < y3

   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. Add Preprocessing

   3. Taylor expanded in y3 around -inf 54.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -7.4 \cdot 10^{+132}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -1.2 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y3 \leq -4.7 \cdot 10^{-18}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.4 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.4 \cdot 10^{-275}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-266}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{-199}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{+43}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+195}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.0305:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-158}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* z (- (* c i) (* a b))))))
   (if (<= a -1.8e+195)
     (* a (* b (- (* x y) (* z t))))
     (if (<= a -9.5e+131)
       t_1
       (if (<= a -0.0305)
         (- (* x (* y (- (* a b) (* c i)))) (* t (* y2 (- (* c y4) (* a y5)))))
         (if (<= a -4.3e-92)
           (* i (* y1 (- (* x j) (* z k))))
           (if (<= a -1.05e-173)
             (* c (* y0 (- (* x y2) (* z y3))))
             (if (<= a -3.8e-262)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= a 1.75e-224)
                 (* b (* j (- (* t y4) (* x y0))))
                 (if (<= a 4.9e-158)
                   (* y0 (* y3 (- (* j y5) (* z c))))
                   (if (<= a 8.5e+59)
                     (+
                      (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
                      (* b (* y4 (- (* t j) (* y k)))))
                     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 = t * (z * ((c * i) - (a * b)));
	double tmp;
	if (a <= -1.8e+195) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (a <= -9.5e+131) {
		tmp = t_1;
	} else if (a <= -0.0305) {
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * ((c * y4) - (a * y5))));
	} else if (a <= -4.3e-92) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= -1.05e-173) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -3.8e-262) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (a <= 1.75e-224) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.9e-158) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 8.5e+59) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (b * (y4 * ((t * j) - (y * k))));
	} 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 = t * (z * ((c * i) - (a * b)))
    if (a <= (-1.8d+195)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (a <= (-9.5d+131)) then
        tmp = t_1
    else if (a <= (-0.0305d0)) then
        tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * ((c * y4) - (a * y5))))
    else if (a <= (-4.3d-92)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= (-1.05d-173)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (a <= (-3.8d-262)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (a <= 1.75d-224) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (a <= 4.9d-158) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (a <= 8.5d+59) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (b * (y4 * ((t * j) - (y * k))))
    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 = t * (z * ((c * i) - (a * b)));
	double tmp;
	if (a <= -1.8e+195) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (a <= -9.5e+131) {
		tmp = t_1;
	} else if (a <= -0.0305) {
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * ((c * y4) - (a * y5))));
	} else if (a <= -4.3e-92) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= -1.05e-173) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -3.8e-262) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (a <= 1.75e-224) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.9e-158) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 8.5e+59) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (b * (y4 * ((t * j) - (y * k))));
	} 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 = t * (z * ((c * i) - (a * b)))
	tmp = 0
	if a <= -1.8e+195:
		tmp = a * (b * ((x * y) - (z * t)))
	elif a <= -9.5e+131:
		tmp = t_1
	elif a <= -0.0305:
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * ((c * y4) - (a * y5))))
	elif a <= -4.3e-92:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= -1.05e-173:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif a <= -3.8e-262:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif a <= 1.75e-224:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif a <= 4.9e-158:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif a <= 8.5e+59:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (b * (y4 * ((t * j) - (y * k))))
	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(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))))
	tmp = 0.0
	if (a <= -1.8e+195)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -9.5e+131)
		tmp = t_1;
	elseif (a <= -0.0305)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) - Float64(t * Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (a <= -4.3e-92)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= -1.05e-173)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (a <= -3.8e-262)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (a <= 1.75e-224)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (a <= 4.9e-158)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (a <= 8.5e+59)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))));
	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 = t * (z * ((c * i) - (a * b)));
	tmp = 0.0;
	if (a <= -1.8e+195)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (a <= -9.5e+131)
		tmp = t_1;
	elseif (a <= -0.0305)
		tmp = (x * (y * ((a * b) - (c * i)))) - (t * (y2 * ((c * y4) - (a * y5))));
	elseif (a <= -4.3e-92)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= -1.05e-173)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (a <= -3.8e-262)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (a <= 1.75e-224)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (a <= 4.9e-158)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (a <= 8.5e+59)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (b * (y4 * ((t * j) - (y * k))));
	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[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+195], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e+131], t$95$1, If[LessEqual[a, -0.0305], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.3e-92], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e-173], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-262], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-224], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-158], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+59], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -1.7999999999999999e195

   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. Add Preprocessing

   3. Taylor expanded in b around inf 56.9%

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

   4. Taylor expanded in a around inf 61.0%

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

   if -1.7999999999999999e195 < a < -9.50000000000000015e131 or 8.4999999999999999e59 < a

   1. Initial program 20.1%

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

   3. Taylor expanded in t around inf 30.3%

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

      1. +-commutative 30.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 30.3%

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

      3. unsub-neg 30.3%

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

      4. *-commutative 30.3%

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

      5. *-commutative 30.3%

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

   5. Simplified 30.3%

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

   6. Taylor expanded in z around inf 53.1%

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

   if -9.50000000000000015e131 < a < -0.030499999999999999

   1. Initial program 25.4%

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

   3. Taylor expanded in y around inf 41.8%

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

      1. +-commutative 41.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.8%

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

      3. unsub-neg 41.8%

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

      4. *-commutative 41.8%

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

      5. *-commutative 41.8%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in k around 0 54.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y3 around 0 54.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -0.030499999999999999 < a < -4.30000000000000014e-92

   1. Initial program 19.9%

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

   3. Taylor expanded in y1 around -inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

      3. +-commutative 41.2%

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

      4. mul-1-neg 41.2%

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

      5. unsub-neg 41.2%

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

      6. *-commutative 41.2%

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

      7. *-commutative 41.2%

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

      8. *-commutative 41.2%

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

      9. *-commutative 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in i around -inf 60.6%

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

   if -4.30000000000000014e-92 < a < -1.05000000000000001e-173

   1. Initial program 23.1%

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

   3. Taylor expanded in y0 around inf 24.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 24.2%

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

      3. unsub-neg 24.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 24.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.4%

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

   if -1.05000000000000001e-173 < a < -3.8000000000000002e-262

   1. Initial program 37.7%

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

   3. Taylor expanded in y1 around -inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

      3. +-commutative 44.4%

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

      4. mul-1-neg 44.4%

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

      5. unsub-neg 44.4%

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

      6. *-commutative 44.4%

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

      7. *-commutative 44.4%

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

      8. *-commutative 44.4%

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

      9. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y3 around -inf 51.0%

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

   if -3.8000000000000002e-262 < a < 1.75000000000000009e-224

   1. Initial program 33.5%

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

   3. Taylor expanded in j around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in b around inf 53.1%

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

   if 1.75000000000000009e-224 < a < 4.89999999999999993e-158

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 60.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 46.6%

      \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   8. Simplified 46.6%

      \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 4.89999999999999993e-158 < a < 8.4999999999999999e59

   1. Initial program 43.7%

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

   3. Taylor expanded in b around inf 36.8%

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

   4. Taylor expanded in y4 around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+195}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -0.0305:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-158}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_2 := t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t\_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;a \leq -1.9:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-158}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1 + b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))
        (t_2 (* t (* y2 (- (* c y4) (* a y5))))))
   (if (<= a -1e+274)
     (- (* x (* y (- (* a b) (* c i)))) t_2)
     (if (<= a -6.6e+66)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= a -1.9)
         (- t_1 t_2)
         (if (<= a -8.5e-96)
           (* i (* y1 (- (* x j) (* z k))))
           (if (<= a -2.4e-173)
             (* c (* y0 (- (* x y2) (* z y3))))
             (if (<= a -5.5e-262)
               (* y1 (* y3 (- (* z a) (* j y4))))
               (if (<= a 9.5e-225)
                 (* b (* j (- (* t y4) (* x y0))))
                 (if (<= a 4.2e-158)
                   (* y0 (* y3 (- (* j y5) (* z c))))
                   (if (<= a 8e+63)
                     (+ t_1 (* b (* y4 (- (* t j) (* y k)))))
                     (* t (* z (- (* c i) (* a b)))))))))))))))

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 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = t * (y2 * ((c * y4) - (a * y5)));
	double tmp;
	if (a <= -1e+274) {
		tmp = (x * (y * ((a * b) - (c * i)))) - t_2;
	} else if (a <= -6.6e+66) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (a <= -1.9) {
		tmp = t_1 - t_2;
	} else if (a <= -8.5e-96) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= -2.4e-173) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -5.5e-262) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (a <= 9.5e-225) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.2e-158) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 8e+63) {
		tmp = t_1 + (b * (y4 * ((t * j) - (y * k))));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	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 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    t_2 = t * (y2 * ((c * y4) - (a * y5)))
    if (a <= (-1d+274)) then
        tmp = (x * (y * ((a * b) - (c * i)))) - t_2
    else if (a <= (-6.6d+66)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (a <= (-1.9d0)) then
        tmp = t_1 - t_2
    else if (a <= (-8.5d-96)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= (-2.4d-173)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (a <= (-5.5d-262)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (a <= 9.5d-225) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (a <= 4.2d-158) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (a <= 8d+63) then
        tmp = t_1 + (b * (y4 * ((t * j) - (y * k))))
    else
        tmp = t * (z * ((c * i) - (a * b)))
    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 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = t * (y2 * ((c * y4) - (a * y5)));
	double tmp;
	if (a <= -1e+274) {
		tmp = (x * (y * ((a * b) - (c * i)))) - t_2;
	} else if (a <= -6.6e+66) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (a <= -1.9) {
		tmp = t_1 - t_2;
	} else if (a <= -8.5e-96) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= -2.4e-173) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -5.5e-262) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (a <= 9.5e-225) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.2e-158) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 8e+63) {
		tmp = t_1 + (b * (y4 * ((t * j) - (y * k))));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
	t_2 = t * (y2 * ((c * y4) - (a * y5)))
	tmp = 0
	if a <= -1e+274:
		tmp = (x * (y * ((a * b) - (c * i)))) - t_2
	elif a <= -6.6e+66:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif a <= -1.9:
		tmp = t_1 - t_2
	elif a <= -8.5e-96:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= -2.4e-173:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif a <= -5.5e-262:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif a <= 9.5e-225:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif a <= 4.2e-158:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif a <= 8e+63:
		tmp = t_1 + (b * (y4 * ((t * j) - (y * k))))
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	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(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_2 = Float64(t * Float64(y2 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (a <= -1e+274)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) - t_2);
	elseif (a <= -6.6e+66)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (a <= -1.9)
		tmp = Float64(t_1 - t_2);
	elseif (a <= -8.5e-96)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= -2.4e-173)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (a <= -5.5e-262)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (a <= 9.5e-225)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (a <= 4.2e-158)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (a <= 8e+63)
		tmp = Float64(t_1 + Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	t_2 = t * (y2 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (a <= -1e+274)
		tmp = (x * (y * ((a * b) - (c * i)))) - t_2;
	elseif (a <= -6.6e+66)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (a <= -1.9)
		tmp = t_1 - t_2;
	elseif (a <= -8.5e-96)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= -2.4e-173)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (a <= -5.5e-262)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (a <= 9.5e-225)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (a <= 4.2e-158)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (a <= 8e+63)
		tmp = t_1 + (b * (y4 * ((t * j) - (y * k))));
	else
		tmp = t * (z * ((c * i) - (a * b)));
	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[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y2 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+274], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[a, -6.6e+66], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[a, -8.5e-96], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-173], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-262], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-225], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-158], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+63], N[(t$95$1 + N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if a < -9.99999999999999921e273

   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. Add Preprocessing

   3. Taylor expanded in y around inf 33.3%

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

      1. +-commutative 33.3%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.3%

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

      3. unsub-neg 33.3%

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

      4. *-commutative 33.3%

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

      5. *-commutative 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in k around 0 44.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y3 around 0 77.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -9.99999999999999921e273 < a < -6.6000000000000003e66

   1. Initial program 19.5%

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

   3. Taylor expanded in b around inf 46.5%

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

   4. Taylor expanded in z around -inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

   6. Simplified 51.2%

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

   if -6.6000000000000003e66 < a < -1.8999999999999999

   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. Add Preprocessing

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

      4. *-commutative 46.2%

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

      5. *-commutative 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in y around 0 62.1%

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

   if -1.8999999999999999 < a < -8.49999999999999983e-96

   1. Initial program 19.9%

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

   3. Taylor expanded in y1 around -inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

      3. +-commutative 41.2%

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

      4. mul-1-neg 41.2%

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

      5. unsub-neg 41.2%

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

      6. *-commutative 41.2%

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

      7. *-commutative 41.2%

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

      8. *-commutative 41.2%

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

      9. *-commutative 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in i around -inf 60.6%

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

   if -8.49999999999999983e-96 < a < -2.40000000000000017e-173

   1. Initial program 23.1%

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

   3. Taylor expanded in y0 around inf 24.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 24.2%

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

      3. unsub-neg 24.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 24.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 24.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.4%

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

   if -2.40000000000000017e-173 < a < -5.5000000000000004e-262

   1. Initial program 37.7%

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

   3. Taylor expanded in y1 around -inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

      3. +-commutative 44.4%

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

      4. mul-1-neg 44.4%

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

      5. unsub-neg 44.4%

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

      6. *-commutative 44.4%

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

      7. *-commutative 44.4%

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

      8. *-commutative 44.4%

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

      9. *-commutative 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in y3 around -inf 51.0%

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

   if -5.5000000000000004e-262 < a < 9.50000000000000006e-225

   1. Initial program 33.5%

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

   3. Taylor expanded in j around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in b around inf 53.1%

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

   if 9.50000000000000006e-225 < a < 4.19999999999999983e-158

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 60.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 60.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 46.6%

      \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   8. Simplified 46.6%

      \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 4.19999999999999983e-158 < a < 8.00000000000000046e63

   1. Initial program 43.7%

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

   3. Taylor expanded in b around inf 36.8%

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

   4. Taylor expanded in y4 around inf 45.0%

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

   if 8.00000000000000046e63 < a

   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. Add Preprocessing

   3. Taylor expanded in t around inf 26.9%

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

      1. +-commutative 26.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 26.9%

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

      3. unsub-neg 26.9%

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

      4. *-commutative 26.9%

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

      5. *-commutative 26.9%

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

   5. Simplified 26.9%

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

   6. Taylor expanded in z around inf 53.8%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;a \leq -1.9:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-158}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+63}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ t_3 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-127}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-233}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-301}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (- (* k y2) (* j y3)))))
        (t_2 (* t (* z (- (* c i) (* a b)))))
        (t_3 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -4.5e+53)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -2.9e-32)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -8.8e-127)
         t_3
         (if (<= b -7.2e-174)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b -3.5e-233)
             t_3
             (if (<= b -6.8e-264)
               t_1
               (if (<= b -1.22e-278)
                 t_2
                 (if (<= b -4e-301)
                   (* y0 (* y2 (- (* x c) (* k y5))))
                   (if (<= b 2.1e-228)
                     (* y1 (* z (- (* a y3) (* i k))))
                     (if (<= b 5.5e-146)
                       (* b (* x (- (* y a) (* j y0))))
                       (if (<= b 1.85e-50)
                         t_1
                         (if (<= b 1.82e+232)
                           t_2
                           (* j (* b (- (* t y4) (* x 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) {
	double t_1 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = t * (z * ((c * i) - (a * b)));
	double t_3 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -4.5e+53) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.9e-32) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -8.8e-127) {
		tmp = t_3;
	} else if (b <= -7.2e-174) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -3.5e-233) {
		tmp = t_3;
	} else if (b <= -6.8e-264) {
		tmp = t_1;
	} else if (b <= -1.22e-278) {
		tmp = t_2;
	} else if (b <= -4e-301) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (b <= 2.1e-228) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 5.5e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.85e-50) {
		tmp = t_1;
	} else if (b <= 1.82e+232) {
		tmp = t_2;
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 = y1 * (y4 * ((k * y2) - (j * y3)))
    t_2 = t * (z * ((c * i) - (a * b)))
    t_3 = c * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-4.5d+53)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-2.9d-32)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-8.8d-127)) then
        tmp = t_3
    else if (b <= (-7.2d-174)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= (-3.5d-233)) then
        tmp = t_3
    else if (b <= (-6.8d-264)) then
        tmp = t_1
    else if (b <= (-1.22d-278)) then
        tmp = t_2
    else if (b <= (-4d-301)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (b <= 2.1d-228) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 5.5d-146) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 1.85d-50) then
        tmp = t_1
    else if (b <= 1.82d+232) then
        tmp = t_2
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = t * (z * ((c * i) - (a * b)));
	double t_3 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -4.5e+53) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.9e-32) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -8.8e-127) {
		tmp = t_3;
	} else if (b <= -7.2e-174) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -3.5e-233) {
		tmp = t_3;
	} else if (b <= -6.8e-264) {
		tmp = t_1;
	} else if (b <= -1.22e-278) {
		tmp = t_2;
	} else if (b <= -4e-301) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (b <= 2.1e-228) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 5.5e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.85e-50) {
		tmp = t_1;
	} else if (b <= 1.82e+232) {
		tmp = t_2;
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * ((k * y2) - (j * y3)))
	t_2 = t * (z * ((c * i) - (a * b)))
	t_3 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -4.5e+53:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -2.9e-32:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -8.8e-127:
		tmp = t_3
	elif b <= -7.2e-174:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= -3.5e-233:
		tmp = t_3
	elif b <= -6.8e-264:
		tmp = t_1
	elif b <= -1.22e-278:
		tmp = t_2
	elif b <= -4e-301:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif b <= 2.1e-228:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 5.5e-146:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 1.85e-50:
		tmp = t_1
	elif b <= 1.82e+232:
		tmp = t_2
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))))
	t_2 = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))))
	t_3 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -4.5e+53)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -2.9e-32)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -8.8e-127)
		tmp = t_3;
	elseif (b <= -7.2e-174)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= -3.5e-233)
		tmp = t_3;
	elseif (b <= -6.8e-264)
		tmp = t_1;
	elseif (b <= -1.22e-278)
		tmp = t_2;
	elseif (b <= -4e-301)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (b <= 2.1e-228)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 5.5e-146)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 1.85e-50)
		tmp = t_1;
	elseif (b <= 1.82e+232)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 = y1 * (y4 * ((k * y2) - (j * y3)));
	t_2 = t * (z * ((c * i) - (a * b)));
	t_3 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -4.5e+53)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -2.9e-32)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -8.8e-127)
		tmp = t_3;
	elseif (b <= -7.2e-174)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= -3.5e-233)
		tmp = t_3;
	elseif (b <= -6.8e-264)
		tmp = t_1;
	elseif (b <= -1.22e-278)
		tmp = t_2;
	elseif (b <= -4e-301)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (b <= 2.1e-228)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 5.5e-146)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 1.85e-50)
		tmp = t_1;
	elseif (b <= 1.82e+232)
		tmp = t_2;
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+53], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-32], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e-127], t$95$3, If[LessEqual[b, -7.2e-174], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-233], t$95$3, If[LessEqual[b, -6.8e-264], t$95$1, If[LessEqual[b, -1.22e-278], t$95$2, If[LessEqual[b, -4e-301], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-228], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-146], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e-50], t$95$1, If[LessEqual[b, 1.82e+232], t$95$2, N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if b < -4.5000000000000002e53

   1. Initial program 28.2%

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

   3. Taylor expanded in b around inf 54.6%

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

   4. Taylor expanded in a around inf 50.5%

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

   if -4.5000000000000002e53 < b < -2.89999999999999996e-32

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -2.89999999999999996e-32 < b < -8.8000000000000006e-127 or -7.19999999999999997e-174 < b < -3.49999999999999991e-233

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 33.0%

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

      3. unsub-neg 33.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 56.9%

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

   if -8.8000000000000006e-127 < b < -7.19999999999999997e-174

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -3.49999999999999991e-233 < b < -6.7999999999999997e-264 or 5.49999999999999998e-146 < b < 1.85e-50

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 53.4%

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

      1. associate-*r* 53.4%

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

      2. neg-mul-1 53.4%

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

      3. +-commutative 53.4%

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

      4. mul-1-neg 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-commutative 53.4%

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

      7. *-commutative 53.4%

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

      8. *-commutative 53.4%

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

      9. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y4 around -inf 66.8%

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

   if -6.7999999999999997e-264 < b < -1.22e-278 or 1.85e-50 < b < 1.82e232

   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. Add Preprocessing

   3. Taylor expanded in t around inf 43.7%

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

      1. +-commutative 43.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

      4. *-commutative 43.7%

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

      5. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in z around inf 49.3%

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

   if -1.22e-278 < b < -4.00000000000000027e-301

   1. Initial program 72.5%

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

   3. Taylor expanded in y0 around inf 43.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 43.2%

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

      3. unsub-neg 43.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 43.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 43.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 43.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 43.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 57.8%

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

   if -4.00000000000000027e-301 < b < 2.09999999999999991e-228

   1. Initial program 24.9%

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

   3. Taylor expanded in y1 around -inf 50.1%

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

      1. associate-*r* 50.1%

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

      2. neg-mul-1 50.1%

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

      3. +-commutative 50.1%

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

      4. mul-1-neg 50.1%

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

      5. unsub-neg 50.1%

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

      6. *-commutative 50.1%

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

      7. *-commutative 50.1%

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

      8. *-commutative 50.1%

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

      9. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around -inf 66.6%

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

   if 2.09999999999999991e-228 < b < 5.49999999999999998e-146

   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. Add Preprocessing

   3. Taylor expanded in b around inf 24.3%

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

   4. Taylor expanded in x around inf 48.2%

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

   if 1.82e232 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

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

      1. +-commutative 40.2%

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

      2. mul-1-neg 40.2%

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

      3. unsub-neg 40.2%

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

      4. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in b around inf 75.3%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-264}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-278}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-301}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t\_1\right)\\ t_3 := y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_4 := t \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_5 := j \cdot \left(\left(t\_4 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -7.2 \cdot 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;j \cdot t\_4\\ \mathbf{elif}\;y0 \leq -8.2 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{-297}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(t\_1 - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (- (* y y3) (* t y2))))
        (t_2
         (*
          y4
          (+ (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3)))) t_1)))
        (t_3
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
           (* b (- (* z k) (* x j))))))
        (t_4 (* t (- (* b y4) (* i y5))))
        (t_5
         (*
          j
          (+
           (+ t_4 (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= y0 -7.2e+35)
     t_3
     (if (<= y0 -1.02e-106)
       t_2
       (if (<= y0 -8.5e-186)
         (* j t_4)
         (if (<= y0 -8.2e-282)
           (* t (* z (- (* c i) (* a b))))
           (if (<= y0 -1.7e-297)
             t_5
             (if (<= y0 1.65e-224)
               t_2
               (if (<= y0 9.5e-74)
                 t_5
                 (if (<= y0 6.5e+98)
                   (* y4 (- t_1 (* j (* y1 y3))))
                   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 = c * ((y * y3) - (t * y2));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	double t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_4 = t * ((b * y4) - (i * y5));
	double t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y0 <= -7.2e+35) {
		tmp = t_3;
	} else if (y0 <= -1.02e-106) {
		tmp = t_2;
	} else if (y0 <= -8.5e-186) {
		tmp = j * t_4;
	} else if (y0 <= -8.2e-282) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= -1.7e-297) {
		tmp = t_5;
	} else if (y0 <= 1.65e-224) {
		tmp = t_2;
	} else if (y0 <= 9.5e-74) {
		tmp = t_5;
	} else if (y0 <= 6.5e+98) {
		tmp = y4 * (t_1 - (j * (y1 * y3)));
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = c * ((y * y3) - (t * y2))
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
    t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    t_4 = t * ((b * y4) - (i * y5))
    t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    if (y0 <= (-7.2d+35)) then
        tmp = t_3
    else if (y0 <= (-1.02d-106)) then
        tmp = t_2
    else if (y0 <= (-8.5d-186)) then
        tmp = j * t_4
    else if (y0 <= (-8.2d-282)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y0 <= (-1.7d-297)) then
        tmp = t_5
    else if (y0 <= 1.65d-224) then
        tmp = t_2
    else if (y0 <= 9.5d-74) then
        tmp = t_5
    else if (y0 <= 6.5d+98) then
        tmp = y4 * (t_1 - (j * (y1 * y3)))
    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 = c * ((y * y3) - (t * y2));
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	double t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_4 = t * ((b * y4) - (i * y5));
	double t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y0 <= -7.2e+35) {
		tmp = t_3;
	} else if (y0 <= -1.02e-106) {
		tmp = t_2;
	} else if (y0 <= -8.5e-186) {
		tmp = j * t_4;
	} else if (y0 <= -8.2e-282) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= -1.7e-297) {
		tmp = t_5;
	} else if (y0 <= 1.65e-224) {
		tmp = t_2;
	} else if (y0 <= 9.5e-74) {
		tmp = t_5;
	} else if (y0 <= 6.5e+98) {
		tmp = y4 * (t_1 - (j * (y1 * y3)));
	} 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 = c * ((y * y3) - (t * y2))
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
	t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	t_4 = t * ((b * y4) - (i * y5))
	t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if y0 <= -7.2e+35:
		tmp = t_3
	elif y0 <= -1.02e-106:
		tmp = t_2
	elif y0 <= -8.5e-186:
		tmp = j * t_4
	elif y0 <= -8.2e-282:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y0 <= -1.7e-297:
		tmp = t_5
	elif y0 <= 1.65e-224:
		tmp = t_2
	elif y0 <= 9.5e-74:
		tmp = t_5
	elif y0 <= 6.5e+98:
		tmp = y4 * (t_1 - (j * (y1 * y3)))
	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(c * Float64(Float64(y * y3) - Float64(t * y2)))
	t_2 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_1))
	t_3 = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_4 = Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))
	t_5 = Float64(j * Float64(Float64(t_4 + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y0 <= -7.2e+35)
		tmp = t_3;
	elseif (y0 <= -1.02e-106)
		tmp = t_2;
	elseif (y0 <= -8.5e-186)
		tmp = Float64(j * t_4);
	elseif (y0 <= -8.2e-282)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y0 <= -1.7e-297)
		tmp = t_5;
	elseif (y0 <= 1.65e-224)
		tmp = t_2;
	elseif (y0 <= 9.5e-74)
		tmp = t_5;
	elseif (y0 <= 6.5e+98)
		tmp = Float64(y4 * Float64(t_1 - Float64(j * Float64(y1 * y3))));
	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 = c * ((y * y3) - (t * y2));
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	t_4 = t * ((b * y4) - (i * y5));
	t_5 = j * ((t_4 + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y0 <= -7.2e+35)
		tmp = t_3;
	elseif (y0 <= -1.02e-106)
		tmp = t_2;
	elseif (y0 <= -8.5e-186)
		tmp = j * t_4;
	elseif (y0 <= -8.2e-282)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y0 <= -1.7e-297)
		tmp = t_5;
	elseif (y0 <= 1.65e-224)
		tmp = t_2;
	elseif (y0 <= 9.5e-74)
		tmp = t_5;
	elseif (y0 <= 6.5e+98)
		tmp = y4 * (t_1 - (j * (y1 * y3)));
	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[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(j * N[(N[(t$95$4 + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7.2e+35], t$95$3, If[LessEqual[y0, -1.02e-106], t$95$2, If[LessEqual[y0, -8.5e-186], N[(j * t$95$4), $MachinePrecision], If[LessEqual[y0, -8.2e-282], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.7e-297], t$95$5, If[LessEqual[y0, 1.65e-224], t$95$2, If[LessEqual[y0, 9.5e-74], t$95$5, If[LessEqual[y0, 6.5e+98], N[(y4 * N[(t$95$1 - N[(j * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -7.2000000000000001e35 or 6.4999999999999999e98 < y0

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 55.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 55.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 55.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 55.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 55.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 55.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   if -7.2000000000000001e35 < y0 < -1.02e-106 or -1.69999999999999991e-297 < y0 < 1.6500000000000001e-224

   1. Initial program 35.4%

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

   3. Taylor expanded in y4 around inf 55.9%

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

   if -1.02e-106 < y0 < -8.4999999999999994e-186

   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. Add Preprocessing

   3. Taylor expanded in j around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in t around inf 65.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -8.4999999999999994e-186 < y0 < -8.19999999999999954e-282

   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. Add Preprocessing

   3. Taylor expanded in t around inf 47.5%

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

      1. +-commutative 47.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

      5. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -8.19999999999999954e-282 < y0 < -1.69999999999999991e-297 or 1.6500000000000001e-224 < y0 < 9.5000000000000007e-74

   1. Initial program 40.7%

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

   3. Taylor expanded in j around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if 9.5000000000000007e-74 < y0 < 6.4999999999999999e98

   1. Initial program 24.9%

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

   3. Taylor expanded in y around inf 32.0%

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

      1. +-commutative 32.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 32.0%

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

      3. unsub-neg 32.0%

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

      4. *-commutative 32.0%

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

      5. *-commutative 32.0%

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

   5. Simplified 32.0%

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

   6. Taylor expanded in k around 0 21.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 46.7%

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

      1. associate-*r* 46.7%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 46.7%

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

      3. *-commutative 46.7%

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

   9. Simplified 46.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.2 \cdot 10^{+35}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -8.2 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-224}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right) - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-27}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.62 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-234}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-230}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (- (* k y2) (* j y3)))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -1.1e+54)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -6.8e-27)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -3.15e-127)
         t_2
         (if (<= b -1.62e-177)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b -6e-234)
             t_2
             (if (<= b -5.2e-262)
               t_1
               (if (<= b -3.8e-301)
                 (* (* t c) (- (* z i) (* y2 y4)))
                 (if (<= b 3.3e-230)
                   (* y1 (* z (- (* a y3) (* i k))))
                   (if (<= b 6e-146)
                     (* b (* x (- (* y a) (* j y0))))
                     (if (<= b 4.4e-51)
                       t_1
                       (if (<= b 3.7e+232)
                         (* t (* z (- (* c i) (* a b))))
                         (* j (* b (- (* t y4) (* x 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) {
	double t_1 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.1e+54) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -6.8e-27) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -3.15e-127) {
		tmp = t_2;
	} else if (b <= -1.62e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -6e-234) {
		tmp = t_2;
	} else if (b <= -5.2e-262) {
		tmp = t_1;
	} else if (b <= -3.8e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 3.3e-230) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 6e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 4.4e-51) {
		tmp = t_1;
	} else if (b <= 3.7e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 = y1 * (y4 * ((k * y2) - (j * y3)))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-1.1d+54)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-6.8d-27)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-3.15d-127)) then
        tmp = t_2
    else if (b <= (-1.62d-177)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= (-6d-234)) then
        tmp = t_2
    else if (b <= (-5.2d-262)) then
        tmp = t_1
    else if (b <= (-3.8d-301)) then
        tmp = (t * c) * ((z * i) - (y2 * y4))
    else if (b <= 3.3d-230) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 6d-146) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 4.4d-51) then
        tmp = t_1
    else if (b <= 3.7d+232) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.1e+54) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -6.8e-27) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -3.15e-127) {
		tmp = t_2;
	} else if (b <= -1.62e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -6e-234) {
		tmp = t_2;
	} else if (b <= -5.2e-262) {
		tmp = t_1;
	} else if (b <= -3.8e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 3.3e-230) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 6e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 4.4e-51) {
		tmp = t_1;
	} else if (b <= 3.7e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * ((k * y2) - (j * y3)))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -1.1e+54:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -6.8e-27:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -3.15e-127:
		tmp = t_2
	elif b <= -1.62e-177:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= -6e-234:
		tmp = t_2
	elif b <= -5.2e-262:
		tmp = t_1
	elif b <= -3.8e-301:
		tmp = (t * c) * ((z * i) - (y2 * y4))
	elif b <= 3.3e-230:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 6e-146:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 4.4e-51:
		tmp = t_1
	elif b <= 3.7e+232:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -1.1e+54)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -6.8e-27)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -3.15e-127)
		tmp = t_2;
	elseif (b <= -1.62e-177)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= -6e-234)
		tmp = t_2;
	elseif (b <= -5.2e-262)
		tmp = t_1;
	elseif (b <= -3.8e-301)
		tmp = Float64(Float64(t * c) * Float64(Float64(z * i) - Float64(y2 * y4)));
	elseif (b <= 3.3e-230)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 6e-146)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 4.4e-51)
		tmp = t_1;
	elseif (b <= 3.7e+232)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 = y1 * (y4 * ((k * y2) - (j * y3)));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -1.1e+54)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -6.8e-27)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -3.15e-127)
		tmp = t_2;
	elseif (b <= -1.62e-177)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= -6e-234)
		tmp = t_2;
	elseif (b <= -5.2e-262)
		tmp = t_1;
	elseif (b <= -3.8e-301)
		tmp = (t * c) * ((z * i) - (y2 * y4));
	elseif (b <= 3.3e-230)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 6e-146)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 4.4e-51)
		tmp = t_1;
	elseif (b <= 3.7e+232)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+54], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.8e-27], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.15e-127], t$95$2, If[LessEqual[b, -1.62e-177], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e-234], t$95$2, If[LessEqual[b, -5.2e-262], t$95$1, If[LessEqual[b, -3.8e-301], N[(N[(t * c), $MachinePrecision] * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-230], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-146], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-51], t$95$1, If[LessEqual[b, 3.7e+232], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if b < -1.09999999999999995e54

   1. Initial program 28.2%

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

   3. Taylor expanded in b around inf 54.6%

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

   4. Taylor expanded in a around inf 50.5%

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

   if -1.09999999999999995e54 < b < -6.7999999999999994e-27

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -6.7999999999999994e-27 < b < -3.1499999999999999e-127 or -1.6199999999999999e-177 < b < -5.99999999999999975e-234

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 34.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 34.0%

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

      3. unsub-neg 34.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 34.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 34.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 34.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 55.6%

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

   if -3.1499999999999999e-127 < b < -1.6199999999999999e-177

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.4%

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

      1. +-commutative 40.4%

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

      2. mul-1-neg 40.4%

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

      3. unsub-neg 40.4%

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

      4. *-commutative 40.4%

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

   5. Simplified 40.4%

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

   6. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -5.99999999999999975e-234 < b < -5.1999999999999998e-262 or 6.00000000000000038e-146 < b < 4.4e-51

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 53.4%

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

      1. associate-*r* 53.4%

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

      2. neg-mul-1 53.4%

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

      3. +-commutative 53.4%

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

      4. mul-1-neg 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-commutative 53.4%

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

      7. *-commutative 53.4%

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

      8. *-commutative 53.4%

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

      9. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y4 around -inf 66.8%

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

   if -5.1999999999999998e-262 < b < -3.79999999999999996e-301

   1. Initial program 64.3%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. +-commutative 64.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in c around -inf 47.6%

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

      1. associate-*r* 47.6%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)} \]

      2. *-commutative 47.6%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \]

      3. +-commutative 47.6%

         \[\leadsto \left(t \cdot c\right) \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \]

      4. mul-1-neg 47.6%

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

      5. unsub-neg 47.6%

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

   8. Simplified 47.6%

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

   if -3.79999999999999996e-301 < b < 3.29999999999999994e-230

   1. Initial program 24.9%

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

   3. Taylor expanded in y1 around -inf 50.1%

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

      1. associate-*r* 50.1%

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

      2. neg-mul-1 50.1%

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

      3. +-commutative 50.1%

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

      4. mul-1-neg 50.1%

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

      5. unsub-neg 50.1%

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

      6. *-commutative 50.1%

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

      7. *-commutative 50.1%

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

      8. *-commutative 50.1%

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

      9. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around -inf 66.6%

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

   if 3.29999999999999994e-230 < b < 6.00000000000000038e-146

   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. Add Preprocessing

   3. Taylor expanded in b around inf 24.3%

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

   4. Taylor expanded in x around inf 48.2%

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

   if 4.4e-51 < b < 3.69999999999999973e232

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

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

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in z around inf 49.0%

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

   if 3.69999999999999973e232 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

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

      1. +-commutative 40.2%

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

      2. mul-1-neg 40.2%

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

      3. unsub-neg 40.2%

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

      4. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in b around inf 75.3%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-27}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -1.62 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-234}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-230}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-140}:\\ \;\;\;\;t\_3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot t\_2\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-299}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot t\_2\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot t\_3 - b \cdot \left(y \cdot k\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* z (- (* c i) (* a b)))))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (- (* k y2) (* j y3))))
   (if (<= x -9.4e+86)
     (* i (* y1 (- (* x j) (* z k))))
     (if (<= x -1.7e-14)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= x -4.6e-140)
         (- (* t_3 (- (* y1 y4) (* y0 y5))) (* t (* y2 t_2)))
         (if (<= x -8.5e-204)
           t_1
           (if (<= x -2.6e-299)
             (* y3 (+ (* j (- (* y0 y5) (* y1 y4))) (* y t_2)))
             (if (<= x 2.9e-257)
               t_1
               (if (<= x 1.25e+149)
                 (*
                  y4
                  (+ (- (* y1 t_3) (* b (* y k))) (* c (- (* y y3) (* t y2)))))
                 (* b (* x (- (* y a) (* j 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) {
	double t_1 = t * (z * ((c * i) - (a * b)));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (k * y2) - (j * y3);
	double tmp;
	if (x <= -9.4e+86) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= -1.7e-14) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= -4.6e-140) {
		tmp = (t_3 * ((y1 * y4) - (y0 * y5))) - (t * (y2 * t_2));
	} else if (x <= -8.5e-204) {
		tmp = t_1;
	} else if (x <= -2.6e-299) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * t_2));
	} else if (x <= 2.9e-257) {
		tmp = t_1;
	} else if (x <= 1.25e+149) {
		tmp = y4 * (((y1 * t_3) - (b * (y * k))) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	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 = t * (z * ((c * i) - (a * b)))
    t_2 = (c * y4) - (a * y5)
    t_3 = (k * y2) - (j * y3)
    if (x <= (-9.4d+86)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (x <= (-1.7d-14)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (x <= (-4.6d-140)) then
        tmp = (t_3 * ((y1 * y4) - (y0 * y5))) - (t * (y2 * t_2))
    else if (x <= (-8.5d-204)) then
        tmp = t_1
    else if (x <= (-2.6d-299)) then
        tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * t_2))
    else if (x <= 2.9d-257) then
        tmp = t_1
    else if (x <= 1.25d+149) then
        tmp = y4 * (((y1 * t_3) - (b * (y * k))) + (c * ((y * y3) - (t * y2))))
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    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 * (z * ((c * i) - (a * b)));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (k * y2) - (j * y3);
	double tmp;
	if (x <= -9.4e+86) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (x <= -1.7e-14) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= -4.6e-140) {
		tmp = (t_3 * ((y1 * y4) - (y0 * y5))) - (t * (y2 * t_2));
	} else if (x <= -8.5e-204) {
		tmp = t_1;
	} else if (x <= -2.6e-299) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * t_2));
	} else if (x <= 2.9e-257) {
		tmp = t_1;
	} else if (x <= 1.25e+149) {
		tmp = y4 * (((y1 * t_3) - (b * (y * k))) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (z * ((c * i) - (a * b)))
	t_2 = (c * y4) - (a * y5)
	t_3 = (k * y2) - (j * y3)
	tmp = 0
	if x <= -9.4e+86:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif x <= -1.7e-14:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif x <= -4.6e-140:
		tmp = (t_3 * ((y1 * y4) - (y0 * y5))) - (t * (y2 * t_2))
	elif x <= -8.5e-204:
		tmp = t_1
	elif x <= -2.6e-299:
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * t_2))
	elif x <= 2.9e-257:
		tmp = t_1
	elif x <= 1.25e+149:
		tmp = y4 * (((y1 * t_3) - (b * (y * k))) + (c * ((y * y3) - (t * y2))))
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (x <= -9.4e+86)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (x <= -1.7e-14)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (x <= -4.6e-140)
		tmp = Float64(Float64(t_3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(t * Float64(y2 * t_2)));
	elseif (x <= -8.5e-204)
		tmp = t_1;
	elseif (x <= -2.6e-299)
		tmp = Float64(y3 * Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(y * t_2)));
	elseif (x <= 2.9e-257)
		tmp = t_1;
	elseif (x <= 1.25e+149)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * t_3) - Float64(b * Float64(y * k))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	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 * (z * ((c * i) - (a * b)));
	t_2 = (c * y4) - (a * y5);
	t_3 = (k * y2) - (j * y3);
	tmp = 0.0;
	if (x <= -9.4e+86)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (x <= -1.7e-14)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (x <= -4.6e-140)
		tmp = (t_3 * ((y1 * y4) - (y0 * y5))) - (t * (y2 * t_2));
	elseif (x <= -8.5e-204)
		tmp = t_1;
	elseif (x <= -2.6e-299)
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (y * t_2));
	elseif (x <= 2.9e-257)
		tmp = t_1;
	elseif (x <= 1.25e+149)
		tmp = y4 * (((y1 * t_3) - (b * (y * k))) + (c * ((y * y3) - (t * y2))));
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	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[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.4e+86], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-14], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e-140], N[(N[(t$95$3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-204], t$95$1, If[LessEqual[x, -2.6e-299], N[(y3 * N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-257], t$95$1, If[LessEqual[x, 1.25e+149], N[(y4 * N[(N[(N[(y1 * t$95$3), $MachinePrecision] - N[(b * N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -9.4000000000000004e86

   1. Initial program 13.2%

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

   3. Taylor expanded in y1 around -inf 26.0%

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

      1. associate-*r* 26.0%

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

      2. neg-mul-1 26.0%

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

      3. +-commutative 26.0%

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

      4. mul-1-neg 26.0%

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

      5. unsub-neg 26.0%

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

      6. *-commutative 26.0%

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

      7. *-commutative 26.0%

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

      8. *-commutative 26.0%

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

      9. *-commutative 26.0%

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

   5. Simplified 26.0%

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

   6. Taylor expanded in i around -inf 51.7%

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

   if -9.4000000000000004e86 < x < -1.70000000000000001e-14

   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. Add Preprocessing

   3. Taylor expanded in b around inf 33.3%

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

   4. Taylor expanded in y around inf 45.2%

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

   if -1.70000000000000001e-14 < x < -4.6000000000000002e-140

   1. Initial program 43.7%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. +-commutative 50.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. *-commutative 50.1%

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

      5. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around 0 69.4%

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

   if -4.6000000000000002e-140 < x < -8.4999999999999997e-204 or -2.5999999999999999e-299 < x < 2.9000000000000002e-257

   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. Add Preprocessing

   3. Taylor expanded in t around inf 57.2%

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

      1. +-commutative 57.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

      4. *-commutative 57.2%

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

      5. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in z around inf 67.2%

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

   if -8.4999999999999997e-204 < x < -2.5999999999999999e-299

   1. Initial program 28.1%

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

   3. Taylor expanded in y around inf 39.4%

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

      1. +-commutative 39.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 39.4%

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

      3. unsub-neg 39.4%

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

      4. *-commutative 39.4%

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

      5. *-commutative 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in y3 around -inf 50.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   if 2.9000000000000002e-257 < x < 1.24999999999999998e149

   1. Initial program 32.6%

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

   3. Taylor expanded in y around inf 41.0%

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

      1. +-commutative 41.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in y4 around inf 44.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-1 \cdot \left(b \cdot \left(k \cdot y\right)\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.24999999999999998e149 < x

   1. Initial program 30.6%

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

   3. Taylor expanded in b around inf 36.4%

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

   4. Taylor expanded in x around inf 56.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-140}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-299}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-227}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y4 (- (* k y2) (* j y3)))))
        (t_2 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -6e+52)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -2.6e-26)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -1.7e-126)
         t_2
         (if (<= b -6.8e-175)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b -3.3e-233)
             t_2
             (if (<= b -1.35e-275)
               t_1
               (if (<= b 7.8e-227)
                 (* y1 (* y3 (- (* z a) (* j y4))))
                 (if (<= b 4.5e-144)
                   (* b (* x (- (* y a) (* j y0))))
                   (if (<= b 7e-51)
                     t_1
                     (if (<= b 1.65e+231)
                       (* t (* z (- (* c i) (* a b))))
                       (* j (* b (- (* t y4) (* x 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) {
	double t_1 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -6e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.6e-26) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -1.7e-126) {
		tmp = t_2;
	} else if (b <= -6.8e-175) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -3.3e-233) {
		tmp = t_2;
	} else if (b <= -1.35e-275) {
		tmp = t_1;
	} else if (b <= 7.8e-227) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= 4.5e-144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 7e-51) {
		tmp = t_1;
	} else if (b <= 1.65e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 = y1 * (y4 * ((k * y2) - (j * y3)))
    t_2 = c * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-6d+52)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-2.6d-26)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-1.7d-126)) then
        tmp = t_2
    else if (b <= (-6.8d-175)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= (-3.3d-233)) then
        tmp = t_2
    else if (b <= (-1.35d-275)) then
        tmp = t_1
    else if (b <= 7.8d-227) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (b <= 4.5d-144) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 7d-51) then
        tmp = t_1
    else if (b <= 1.65d+231) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 = y1 * (y4 * ((k * y2) - (j * y3)));
	double t_2 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -6e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -2.6e-26) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -1.7e-126) {
		tmp = t_2;
	} else if (b <= -6.8e-175) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= -3.3e-233) {
		tmp = t_2;
	} else if (b <= -1.35e-275) {
		tmp = t_1;
	} else if (b <= 7.8e-227) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= 4.5e-144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 7e-51) {
		tmp = t_1;
	} else if (b <= 1.65e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (y4 * ((k * y2) - (j * y3)))
	t_2 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -6e+52:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -2.6e-26:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -1.7e-126:
		tmp = t_2
	elif b <= -6.8e-175:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= -3.3e-233:
		tmp = t_2
	elif b <= -1.35e-275:
		tmp = t_1
	elif b <= 7.8e-227:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif b <= 4.5e-144:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 7e-51:
		tmp = t_1
	elif b <= 1.65e+231:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))))
	t_2 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -6e+52)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -2.6e-26)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -1.7e-126)
		tmp = t_2;
	elseif (b <= -6.8e-175)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= -3.3e-233)
		tmp = t_2;
	elseif (b <= -1.35e-275)
		tmp = t_1;
	elseif (b <= 7.8e-227)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (b <= 4.5e-144)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 7e-51)
		tmp = t_1;
	elseif (b <= 1.65e+231)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 = y1 * (y4 * ((k * y2) - (j * y3)));
	t_2 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -6e+52)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -2.6e-26)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -1.7e-126)
		tmp = t_2;
	elseif (b <= -6.8e-175)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= -3.3e-233)
		tmp = t_2;
	elseif (b <= -1.35e-275)
		tmp = t_1;
	elseif (b <= 7.8e-227)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (b <= 4.5e-144)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 7e-51)
		tmp = t_1;
	elseif (b <= 1.65e+231)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+52], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-26], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-126], t$95$2, If[LessEqual[b, -6.8e-175], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-233], t$95$2, If[LessEqual[b, -1.35e-275], t$95$1, If[LessEqual[b, 7.8e-227], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-144], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-51], t$95$1, If[LessEqual[b, 1.65e+231], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -6e52

   1. Initial program 28.2%

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

   3. Taylor expanded in b around inf 54.6%

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

   4. Taylor expanded in a around inf 50.5%

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

   if -6e52 < b < -2.6000000000000001e-26

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -2.6000000000000001e-26 < b < -1.7e-126 or -6.8e-175 < b < -3.3e-233

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 33.0%

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

      3. unsub-neg 33.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 56.9%

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

   if -1.7e-126 < b < -6.8e-175

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -3.3e-233 < b < -1.34999999999999997e-275 or 4.4999999999999998e-144 < b < 6.9999999999999995e-51

   1. Initial program 39.6%

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

   3. Taylor expanded in y1 around -inf 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

      3. +-commutative 47.4%

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

      4. mul-1-neg 47.4%

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

      5. unsub-neg 47.4%

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

      6. *-commutative 47.4%

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

      7. *-commutative 47.4%

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

      8. *-commutative 47.4%

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

      9. *-commutative 47.4%

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

   5. Simplified 47.4%

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

   6. Taylor expanded in y4 around -inf 59.3%

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

   if -1.34999999999999997e-275 < b < 7.7999999999999999e-227

   1. Initial program 40.3%

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

   3. Taylor expanded in y1 around -inf 55.6%

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

      1. associate-*r* 55.6%

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

      2. neg-mul-1 55.6%

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

      3. +-commutative 55.6%

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

      4. mul-1-neg 55.6%

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

      5. unsub-neg 55.6%

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

      6. *-commutative 55.6%

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

      7. *-commutative 55.6%

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

      8. *-commutative 55.6%

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

      9. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y3 around -inf 41.1%

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

   if 7.7999999999999999e-227 < b < 4.4999999999999998e-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. Add Preprocessing

   3. Taylor expanded in b around inf 24.3%

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

   4. Taylor expanded in x around inf 48.2%

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

   if 6.9999999999999995e-51 < b < 1.6499999999999999e231

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

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

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in z around inf 49.0%

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

   if 1.6499999999999999e231 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

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

      1. +-commutative 40.2%

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

      2. mul-1-neg 40.2%

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

      3. unsub-neg 40.2%

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

      4. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in b around inf 75.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-26}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-275}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-227}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= z -2.8e+154)
     (* t (* z (- (* c i) (* a b))))
     (if (<= z -6.5e+115)
       (+
        (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
        (* i (* y (- (* k y5) (* x c)))))
       (if (<= z -5.8e-10)
         (* y0 (* b (- (* z k) (* x j))))
         (if (<= z 5.8e-236)
           t_1
           (if (<= z 2.5e-74)
             (* (* c y4) (- (* y y3) (* t y2)))
             (if (<= z 1.25e+150) t_1 (* y1 (* z (- (* a y3) (* i k))))))))))))

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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (z <= -2.8e+154) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (z <= -6.5e+115) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	} else if (z <= -5.8e-10) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (z <= 5.8e-236) {
		tmp = t_1;
	} else if (z <= 2.5e-74) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (z <= 1.25e+150) {
		tmp = t_1;
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    if (z <= (-2.8d+154)) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (z <= (-6.5d+115)) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))))
    else if (z <= (-5.8d-10)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (z <= 5.8d-236) then
        tmp = t_1
    else if (z <= 2.5d-74) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (z <= 1.25d+150) then
        tmp = t_1
    else
        tmp = y1 * (z * ((a * y3) - (i * k)))
    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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (z <= -2.8e+154) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (z <= -6.5e+115) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	} else if (z <= -5.8e-10) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (z <= 5.8e-236) {
		tmp = t_1;
	} else if (z <= 2.5e-74) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (z <= 1.25e+150) {
		tmp = t_1;
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if z <= -2.8e+154:
		tmp = t * (z * ((c * i) - (a * b)))
	elif z <= -6.5e+115:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))))
	elif z <= -5.8e-10:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif z <= 5.8e-236:
		tmp = t_1
	elif z <= 2.5e-74:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif z <= 1.25e+150:
		tmp = t_1
	else:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (z <= -2.8e+154)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (z <= -6.5e+115)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c)))));
	elseif (z <= -5.8e-10)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (z <= 5.8e-236)
		tmp = t_1;
	elseif (z <= 2.5e-74)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (z <= 1.25e+150)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (z <= -2.8e+154)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (z <= -6.5e+115)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	elseif (z <= -5.8e-10)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (z <= 5.8e-236)
		tmp = t_1;
	elseif (z <= 2.5e-74)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (z <= 1.25e+150)
		tmp = t_1;
	else
		tmp = y1 * (z * ((a * y3) - (i * k)));
	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[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+154], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e+115], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-10], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-236], t$95$1, If[LessEqual[z, 2.5e-74], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+150], t$95$1, N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.7999999999999999e154

   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. Add Preprocessing

   3. Taylor expanded in t around inf 29.7%

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

      1. +-commutative 29.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 29.7%

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

      3. unsub-neg 29.7%

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

      4. *-commutative 29.7%

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

      5. *-commutative 29.7%

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

   5. Simplified 29.7%

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

   6. Taylor expanded in z around inf 65.2%

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

   if -2.7999999999999999e154 < z < -6.49999999999999966e115

   1. Initial program 2.3%

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

   3. Taylor expanded in y around inf 14.8%

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

      1. +-commutative 14.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 14.8%

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

      3. unsub-neg 14.8%

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

      4. *-commutative 14.8%

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

      5. *-commutative 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in i around -inf 89.8%

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

      1. associate-*r* 89.8%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. neg-mul-1 89.8%

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

   8. Simplified 89.8%

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

   if -6.49999999999999966e115 < z < -5.79999999999999962e-10

   1. Initial program 39.8%

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

   3. Taylor expanded in y0 around inf 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in b around inf 52.7%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -5.79999999999999962e-10 < z < 5.8e-236 or 2.49999999999999999e-74 < z < 1.25000000000000002e150

   1. Initial program 33.1%

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

   3. Taylor expanded in j around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   if 5.8e-236 < z < 2.49999999999999999e-74

   1. Initial program 35.4%

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

   3. Taylor expanded in y around inf 38.7%

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

      1. +-commutative 38.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 38.7%

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

      3. unsub-neg 38.7%

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

      4. *-commutative 38.7%

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

      5. *-commutative 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in k around 0 38.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 53.5%

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

      1. associate-*r* 53.5%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 53.5%

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

      3. *-commutative 53.5%

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

   9. Simplified 53.5%

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

   10. Taylor expanded in c around inf 53.8%

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

       1. associate-*r* 53.8%

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

       2. *-commutative 53.8%

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

       3. *-commutative 53.8%

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

       4. *-commutative 53.8%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right) \]

   12. Simplified 53.8%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)} \]

   if 1.25000000000000002e150 < z

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 43.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 43.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 57.3%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ t_2 := b \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+105}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;y0 \cdot t\_2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-35}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* z (- (* c i) (* a b))))) (t_2 (* b (- (* z k) (* x j)))))
   (if (<= z -1.18e+154)
     t_1
     (if (<= z -1.35e+105)
       (+
        (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
        (* i (* y (- (* k y5) (* x c)))))
       (if (<= z -6.2e-10)
         (* y0 t_2)
         (if (<= z 7.6e-236)
           (*
            j
            (+
             (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
             (* x (- (* i y1) (* b y0)))))
           (if (<= z 1.62e-35)
             (* (* c y4) (- (* y y3) (* t y2)))
             (if (<= z 7e+101)
               (*
                y0
                (+
                 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
                 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 = t * (z * ((c * i) - (a * b)));
	double t_2 = b * ((z * k) - (x * j));
	double tmp;
	if (z <= -1.18e+154) {
		tmp = t_1;
	} else if (z <= -1.35e+105) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	} else if (z <= -6.2e-10) {
		tmp = y0 * t_2;
	} else if (z <= 7.6e-236) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (z <= 1.62e-35) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (z <= 7e+101) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + 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 = t * (z * ((c * i) - (a * b)))
    t_2 = b * ((z * k) - (x * j))
    if (z <= (-1.18d+154)) then
        tmp = t_1
    else if (z <= (-1.35d+105)) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))))
    else if (z <= (-6.2d-10)) then
        tmp = y0 * t_2
    else if (z <= 7.6d-236) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (z <= 1.62d-35) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (z <= 7d+101) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + 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 = t * (z * ((c * i) - (a * b)));
	double t_2 = b * ((z * k) - (x * j));
	double tmp;
	if (z <= -1.18e+154) {
		tmp = t_1;
	} else if (z <= -1.35e+105) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	} else if (z <= -6.2e-10) {
		tmp = y0 * t_2;
	} else if (z <= 7.6e-236) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (z <= 1.62e-35) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (z <= 7e+101) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + 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 = t * (z * ((c * i) - (a * b)))
	t_2 = b * ((z * k) - (x * j))
	tmp = 0
	if z <= -1.18e+154:
		tmp = t_1
	elif z <= -1.35e+105:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))))
	elif z <= -6.2e-10:
		tmp = y0 * t_2
	elif z <= 7.6e-236:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif z <= 1.62e-35:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif z <= 7e+101:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + 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(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))))
	t_2 = Float64(b * Float64(Float64(z * k) - Float64(x * j)))
	tmp = 0.0
	if (z <= -1.18e+154)
		tmp = t_1;
	elseif (z <= -1.35e+105)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c)))));
	elseif (z <= -6.2e-10)
		tmp = Float64(y0 * t_2);
	elseif (z <= 7.6e-236)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (z <= 1.62e-35)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (z <= 7e+101)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + 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 = t * (z * ((c * i) - (a * b)));
	t_2 = b * ((z * k) - (x * j));
	tmp = 0.0;
	if (z <= -1.18e+154)
		tmp = t_1;
	elseif (z <= -1.35e+105)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (i * (y * ((k * y5) - (x * c))));
	elseif (z <= -6.2e-10)
		tmp = y0 * t_2;
	elseif (z <= 7.6e-236)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (z <= 1.62e-35)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (z <= 7e+101)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + 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[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e+154], t$95$1, If[LessEqual[z, -1.35e+105], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-10], N[(y0 * t$95$2), $MachinePrecision], If[LessEqual[z, 7.6e-236], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e-35], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+101], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.18000000000000004e154 or 7.00000000000000046e101 < z

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 33.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.2%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 33.2%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 33.2%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 33.2%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 58.4%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]

   if -1.18000000000000004e154 < z < -1.35000000000000008e105

   1. Initial program 2.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 14.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 14.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 14.8%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 14.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 14.8%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 14.8%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 14.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in i around -inf 89.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   7. Step-by-step derivation

      1. associate-*r* 89.8%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. neg-mul-1 89.8%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   8. Simplified 89.8%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot \left(c \cdot x - k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -1.35000000000000008e105 < z < -6.2000000000000003e-10

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 48.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in b around inf 52.7%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -6.2000000000000003e-10 < z < 7.5999999999999998e-236

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 47.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 47.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   if 7.5999999999999998e-236 < z < 1.62000000000000011e-35

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 33.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.8%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 33.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 33.8%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 33.8%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 36.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 49.5%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 49.5%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 49.5%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 49.5%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 49.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in c around inf 52.2%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 52.2%

          \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

       2. *-commutative 52.2%

          \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

       3. *-commutative 52.2%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

       4. *-commutative 52.2%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right) \]

   12. Simplified 52.2%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)} \]

   if 1.62000000000000011e-35 < z < 7.00000000000000046e101

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 59.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 59.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 59.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 59.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 59.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 59.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 59.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+105}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-35}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y4 - x \cdot y0\\ \mathbf{if}\;b \leq -3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(j \cdot t\_1\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-98}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y4) (* x y0))))
   (if (<= b -3e+52)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -5.2e-33)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -1.55e-124)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= b -2.1e-152)
           (* b (* j t_1))
           (if (<= b 2e-234)
             (* y1 (* y3 (- (* z a) (* j y4))))
             (if (<= b 5.5e-146)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= b 1.9e-98)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= b 2.05e-50)
                   (* i (* y1 (- (* x j) (* z k))))
                   (if (<= b 4.1e+231)
                     (* t (* z (- (* c i) (* a b))))
                     (* j (* b 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 = (t * y4) - (x * y0);
	double tmp;
	if (b <= -3e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.2e-33) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -1.55e-124) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= -2.1e-152) {
		tmp = b * (j * t_1);
	} else if (b <= 2e-234) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= 5.5e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.9e-98) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (b <= 2.05e-50) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 4.1e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * 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 = (t * y4) - (x * y0)
    if (b <= (-3d+52)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-5.2d-33)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-1.55d-124)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= (-2.1d-152)) then
        tmp = b * (j * t_1)
    else if (b <= 2d-234) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (b <= 5.5d-146) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 1.9d-98) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (b <= 2.05d-50) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (b <= 4.1d+231) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = j * (b * 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 = (t * y4) - (x * y0);
	double tmp;
	if (b <= -3e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -5.2e-33) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -1.55e-124) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= -2.1e-152) {
		tmp = b * (j * t_1);
	} else if (b <= 2e-234) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= 5.5e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.9e-98) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (b <= 2.05e-50) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 4.1e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * 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 = (t * y4) - (x * y0)
	tmp = 0
	if b <= -3e+52:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -5.2e-33:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -1.55e-124:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= -2.1e-152:
		tmp = b * (j * t_1)
	elif b <= 2e-234:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif b <= 5.5e-146:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 1.9e-98:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif b <= 2.05e-50:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif b <= 4.1e+231:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = j * (b * 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(t * y4) - Float64(x * y0))
	tmp = 0.0
	if (b <= -3e+52)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -5.2e-33)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -1.55e-124)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= -2.1e-152)
		tmp = Float64(b * Float64(j * t_1));
	elseif (b <= 2e-234)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (b <= 5.5e-146)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 1.9e-98)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (b <= 2.05e-50)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (b <= 4.1e+231)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(j * Float64(b * 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 = (t * y4) - (x * y0);
	tmp = 0.0;
	if (b <= -3e+52)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -5.2e-33)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -1.55e-124)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= -2.1e-152)
		tmp = b * (j * t_1);
	elseif (b <= 2e-234)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (b <= 5.5e-146)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 1.9e-98)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (b <= 2.05e-50)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (b <= 4.1e+231)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = j * (b * 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[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+52], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-33], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.55e-124], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-152], N[(b * N[(j * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-234], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-146], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-98], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-50], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+231], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if b < -3e52

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -3e52 < b < -5.19999999999999988e-33

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -5.19999999999999988e-33 < b < -1.5499999999999999e-124

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 25.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 25.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 25.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 25.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 25.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 25.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 25.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 25.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 25.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 55.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.5499999999999999e-124 < b < -2.09999999999999999e-152

   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. Add Preprocessing

   3. Taylor expanded in j around inf 36.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 36.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 47.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -2.09999999999999999e-152 < b < 1.9999999999999999e-234

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 51.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 51.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 51.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 51.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 51.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 40.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   if 1.9999999999999999e-234 < b < 5.49999999999999998e-146

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 23.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 5.49999999999999998e-146 < b < 1.9000000000000002e-98

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 58.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 58.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 58.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 58.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 58.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 58.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 58.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y5 around inf 58.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)} \]

   if 1.9000000000000002e-98 < b < 2.04999999999999993e-50

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 62.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 62.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 62.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 62.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 51.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.04999999999999993e-50 < b < 4.1000000000000003e231

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]

   if 4.1000000000000003e231 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 75.3%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-98}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-52}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
   (if (<= b -4e+120)
     t_1
     (if (<= b -2e-52)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= b -2.3e-102)
         (* a (* t (* y2 y5)))
         (if (<= b -3e-198)
           (* y1 (* y3 (- (* z a) (* j y4))))
           (if (<= b -2.7e-301)
             (* (* t c) (- (* z i) (* y2 y4)))
             (if (<= b 7.2e-233)
               (* y1 (* z (- (* a y3) (* i k))))
               (if (<= b 4.6e-144)
                 (* b (* x (- (* y a) (* j y0))))
                 (if (<= b 1.35e-51)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (if (<= b 6.8e+230)
                     (* t (* z (- (* c i) (* a b))))
                     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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -4e+120) {
		tmp = t_1;
	} else if (b <= -2e-52) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (b <= -2.3e-102) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -3e-198) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= -2.7e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 7.2e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 4.6e-144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.35e-51) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 6.8e+230) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
    if (b <= (-4d+120)) then
        tmp = t_1
    else if (b <= (-2d-52)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (b <= (-2.3d-102)) then
        tmp = a * (t * (y2 * y5))
    else if (b <= (-3d-198)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (b <= (-2.7d-301)) then
        tmp = (t * c) * ((z * i) - (y2 * y4))
    else if (b <= 7.2d-233) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 4.6d-144) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 1.35d-51) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (b <= 6.8d+230) then
        tmp = t * (z * ((c * i) - (a * b)))
    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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -4e+120) {
		tmp = t_1;
	} else if (b <= -2e-52) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (b <= -2.3e-102) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -3e-198) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= -2.7e-301) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (b <= 7.2e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 4.6e-144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.35e-51) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 6.8e+230) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
	tmp = 0
	if b <= -4e+120:
		tmp = t_1
	elif b <= -2e-52:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif b <= -2.3e-102:
		tmp = a * (t * (y2 * y5))
	elif b <= -3e-198:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif b <= -2.7e-301:
		tmp = (t * c) * ((z * i) - (y2 * y4))
	elif b <= 7.2e-233:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 4.6e-144:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 1.35e-51:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif b <= 6.8e+230:
		tmp = t * (z * ((c * i) - (a * b)))
	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(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -4e+120)
		tmp = t_1;
	elseif (b <= -2e-52)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (b <= -2.3e-102)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (b <= -3e-198)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (b <= -2.7e-301)
		tmp = Float64(Float64(t * c) * Float64(Float64(z * i) - Float64(y2 * y4)));
	elseif (b <= 7.2e-233)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 4.6e-144)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 1.35e-51)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (b <= 6.8e+230)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 = j * (b * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (b <= -4e+120)
		tmp = t_1;
	elseif (b <= -2e-52)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (b <= -2.3e-102)
		tmp = a * (t * (y2 * y5));
	elseif (b <= -3e-198)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (b <= -2.7e-301)
		tmp = (t * c) * ((z * i) - (y2 * y4));
	elseif (b <= 7.2e-233)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 4.6e-144)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 1.35e-51)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (b <= 6.8e+230)
		tmp = t * (z * ((c * i) - (a * b)));
	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[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+120], t$95$1, If[LessEqual[b, -2e-52], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-102], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-198], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-301], N[(N[(t * c), $MachinePrecision] * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-233], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e-144], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e-51], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+230], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -3.9999999999999999e120 or 6.79999999999999973e230 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 44.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 65.1%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.9999999999999999e120 < b < -2e-52

   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. Add Preprocessing

   3. Taylor expanded in y around inf 41.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 47.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 41.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 41.9%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in c around inf 42.1%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 42.1%

          \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

       2. *-commutative 42.1%

          \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

       3. *-commutative 42.1%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

       4. *-commutative 42.1%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right) \]

   12. Simplified 42.1%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)} \]

   if -2e-52 < b < -2.29999999999999987e-102

   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. Add Preprocessing

   3. Taylor expanded in y around inf 45.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 45.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 45.6%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 45.6%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 45.6%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 73.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 73.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.29999999999999987e-102 < b < -3.0000000000000001e-198

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 40.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 40.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 44.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   if -3.0000000000000001e-198 < b < -2.7e-301

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.1%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.1%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.1%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.1%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in c around -inf 44.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)} \]

      2. *-commutative 40.9%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right) \]

      3. +-commutative 40.9%

         \[\leadsto \left(t \cdot c\right) \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)} \]

      4. mul-1-neg 40.9%

         \[\leadsto \left(t \cdot c\right) \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right) \]

      5. unsub-neg 40.9%

         \[\leadsto \left(t \cdot c\right) \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)} \]

   8. Simplified 40.9%

      \[\leadsto \color{blue}{\left(t \cdot c\right) \cdot \left(i \cdot z - y2 \cdot y4\right)} \]

   if -2.7e-301 < b < 7.20000000000000014e-233

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 54.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 72.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 7.20000000000000014e-233 < b < 4.6e-144

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 23.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 4.6e-144 < b < 1.3499999999999999e-51

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 54.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 60.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 1.3499999999999999e-51 < b < 6.79999999999999973e230

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-52}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-56}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-182}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-305}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
   (if (<= b -7.2e+121)
     t_1
     (if (<= b -3.8e-56)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= b -5.5e-102)
         (* a (* t (* y2 y5)))
         (if (<= b -1.65e-182)
           (* y1 (* y3 (- (* z a) (* j y4))))
           (if (<= b -1e-305)
             (* (* a y1) (- (* z y3) (* x y2)))
             (if (<= b 6.2e-234)
               (* y1 (* z (- (* a y3) (* i k))))
               (if (<= b 7.2e-146)
                 (* b (* x (- (* y a) (* j y0))))
                 (if (<= b 4.5e-51)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (if (<= b 3.6e+232)
                     (* t (* z (- (* c i) (* a b))))
                     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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -7.2e+121) {
		tmp = t_1;
	} else if (b <= -3.8e-56) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (b <= -5.5e-102) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -1.65e-182) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= -1e-305) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 6.2e-234) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 7.2e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 4.5e-51) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 3.6e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
    if (b <= (-7.2d+121)) then
        tmp = t_1
    else if (b <= (-3.8d-56)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (b <= (-5.5d-102)) then
        tmp = a * (t * (y2 * y5))
    else if (b <= (-1.65d-182)) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (b <= (-1d-305)) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (b <= 6.2d-234) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 7.2d-146) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 4.5d-51) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (b <= 3.6d+232) then
        tmp = t * (z * ((c * i) - (a * b)))
    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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -7.2e+121) {
		tmp = t_1;
	} else if (b <= -3.8e-56) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (b <= -5.5e-102) {
		tmp = a * (t * (y2 * y5));
	} else if (b <= -1.65e-182) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (b <= -1e-305) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 6.2e-234) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 7.2e-146) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 4.5e-51) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 3.6e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
	tmp = 0
	if b <= -7.2e+121:
		tmp = t_1
	elif b <= -3.8e-56:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif b <= -5.5e-102:
		tmp = a * (t * (y2 * y5))
	elif b <= -1.65e-182:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif b <= -1e-305:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif b <= 6.2e-234:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 7.2e-146:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 4.5e-51:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif b <= 3.6e+232:
		tmp = t * (z * ((c * i) - (a * b)))
	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(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -7.2e+121)
		tmp = t_1;
	elseif (b <= -3.8e-56)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (b <= -5.5e-102)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (b <= -1.65e-182)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (b <= -1e-305)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (b <= 6.2e-234)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 7.2e-146)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 4.5e-51)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (b <= 3.6e+232)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 = j * (b * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (b <= -7.2e+121)
		tmp = t_1;
	elseif (b <= -3.8e-56)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (b <= -5.5e-102)
		tmp = a * (t * (y2 * y5));
	elseif (b <= -1.65e-182)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (b <= -1e-305)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (b <= 6.2e-234)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 7.2e-146)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 4.5e-51)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (b <= 3.6e+232)
		tmp = t * (z * ((c * i) - (a * b)));
	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[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+121], t$95$1, If[LessEqual[b, -3.8e-56], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-102], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.65e-182], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-305], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-234], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-146], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-51], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+232], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -7.19999999999999963e121 or 3.59999999999999993e232 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 44.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 65.1%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -7.19999999999999963e121 < b < -3.8000000000000002e-56

   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. Add Preprocessing

   3. Taylor expanded in y around inf 41.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 47.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 41.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 41.9%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in c around inf 42.1%

       \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 42.1%

          \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

       2. *-commutative 42.1%

          \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

       3. *-commutative 42.1%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

       4. *-commutative 42.1%

          \[\leadsto \left(y4 \cdot c\right) \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right) \]

   12. Simplified 42.1%

       \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - y2 \cdot t\right)} \]

   if -3.8000000000000002e-56 < b < -5.4999999999999997e-102

   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. Add Preprocessing

   3. Taylor expanded in y around inf 45.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 45.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 45.6%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 45.6%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 45.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 45.6%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 73.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 73.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -5.4999999999999997e-102 < b < -1.64999999999999998e-182

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 37.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 37.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 37.3%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 37.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.3%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 42.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   if -1.64999999999999998e-182 < b < -9.99999999999999996e-306

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 50.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 50.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.4%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

      2. associate-*r* 47.5%

         \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)} \]

   8. Simplified 47.5%

      \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)} \]

   if -9.99999999999999996e-306 < b < 6.2000000000000003e-234

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 60.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 60.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 60.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 60.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 60.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 70.0%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 6.2000000000000003e-234 < b < 7.19999999999999957e-146

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 23.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 7.19999999999999957e-146 < b < 4.49999999999999974e-51

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 54.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 60.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 4.49999999999999974e-51 < b < 3.59999999999999993e232

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-56}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-182}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-305}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-51}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -3.2e+52)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -8e-24)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -3e-126)
         t_1
         (if (<= b -1.4e-175)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b 1.42e-304)
             t_1
             (if (<= b 1.4e-146)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= b 1.25e+72)
                 (* k (* y2 (- (* y1 y4) (* y0 y5))))
                 (if (<= b 1.8e+104)
                   (* j (* y0 (* y3 y5)))
                   (* j (* b (- (* t y4) (* x 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) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -3.2e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8e-24) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -3e-126) {
		tmp = t_1;
	} else if (b <= -1.4e-175) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.42e-304) {
		tmp = t_1;
	} else if (b <= 1.4e-146) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 1.25e+72) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 1.8e+104) {
		tmp = j * (y0 * (y3 * y5));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-3.2d+52)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-8d-24)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-3d-126)) then
        tmp = t_1
    else if (b <= (-1.4d-175)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 1.42d-304) then
        tmp = t_1
    else if (b <= 1.4d-146) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (b <= 1.25d+72) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (b <= 1.8d+104) then
        tmp = j * (y0 * (y3 * y5))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -3.2e+52) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8e-24) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -3e-126) {
		tmp = t_1;
	} else if (b <= -1.4e-175) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.42e-304) {
		tmp = t_1;
	} else if (b <= 1.4e-146) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 1.25e+72) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 1.8e+104) {
		tmp = j * (y0 * (y3 * y5));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -3.2e+52:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -8e-24:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -3e-126:
		tmp = t_1
	elif b <= -1.4e-175:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 1.42e-304:
		tmp = t_1
	elif b <= 1.4e-146:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif b <= 1.25e+72:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif b <= 1.8e+104:
		tmp = j * (y0 * (y3 * y5))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -3.2e+52)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -8e-24)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -3e-126)
		tmp = t_1;
	elseif (b <= -1.4e-175)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 1.42e-304)
		tmp = t_1;
	elseif (b <= 1.4e-146)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (b <= 1.25e+72)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (b <= 1.8e+104)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -3.2e+52)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -8e-24)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -3e-126)
		tmp = t_1;
	elseif (b <= -1.4e-175)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 1.42e-304)
		tmp = t_1;
	elseif (b <= 1.4e-146)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (b <= 1.25e+72)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (b <= 1.8e+104)
		tmp = j * (y0 * (y3 * y5));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+52], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e-24], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-126], t$95$1, If[LessEqual[b, -1.4e-175], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e-304], t$95$1, If[LessEqual[b, 1.4e-146], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+72], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+104], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -3.2e52

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -3.2e52 < b < -7.99999999999999939e-24

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -7.99999999999999939e-24 < b < -3.0000000000000002e-126 or -1.4e-175 < b < 1.42000000000000007e-304

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -3.0000000000000002e-126 < b < -1.4e-175

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 1.42000000000000007e-304 < b < 1.40000000000000001e-146

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 42.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 1.40000000000000001e-146 < b < 1.24999999999999998e72

   1. Initial program 38.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y2 around inf 42.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 1.24999999999999998e72 < b < 1.8e104

   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. Add Preprocessing

   3. Taylor expanded in y around inf 42.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 42.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 42.9%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 42.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 42.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 42.9%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 42.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y0 around inf 71.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 71.7%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   9. Simplified 71.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]

   if 1.8e104 < b

   1. Initial program 18.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 40.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 54.9%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-146}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-147}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-50}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -2.9e+51)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -1e-32)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -2e-127)
         t_1
         (if (<= b -1.6e-176)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b 4.1e-304)
             t_1
             (if (<= b 1e-147)
               (* i (* y1 (- (* x j) (* z k))))
               (if (<= b 3.7e-50)
                 (* k (* y2 (- (* y1 y4) (* y0 y5))))
                 (if (<= b 1.15e+232)
                   (* t (* z (- (* c i) (* a b))))
                   (* j (* b (- (* t y4) (* x 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) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -2.9e+51) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1e-32) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -2e-127) {
		tmp = t_1;
	} else if (b <= -1.6e-176) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 4.1e-304) {
		tmp = t_1;
	} else if (b <= 1e-147) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 3.7e-50) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 1.15e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-2.9d+51)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-1d-32)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-2d-127)) then
        tmp = t_1
    else if (b <= (-1.6d-176)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 4.1d-304) then
        tmp = t_1
    else if (b <= 1d-147) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (b <= 3.7d-50) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (b <= 1.15d+232) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -2.9e+51) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1e-32) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -2e-127) {
		tmp = t_1;
	} else if (b <= -1.6e-176) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 4.1e-304) {
		tmp = t_1;
	} else if (b <= 1e-147) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (b <= 3.7e-50) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (b <= 1.15e+232) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -2.9e+51:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -1e-32:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -2e-127:
		tmp = t_1
	elif b <= -1.6e-176:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 4.1e-304:
		tmp = t_1
	elif b <= 1e-147:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif b <= 3.7e-50:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif b <= 1.15e+232:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -2.9e+51)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -1e-32)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -2e-127)
		tmp = t_1;
	elseif (b <= -1.6e-176)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 4.1e-304)
		tmp = t_1;
	elseif (b <= 1e-147)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (b <= 3.7e-50)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (b <= 1.15e+232)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -2.9e+51)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -1e-32)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -2e-127)
		tmp = t_1;
	elseif (b <= -1.6e-176)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 4.1e-304)
		tmp = t_1;
	elseif (b <= 1e-147)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (b <= 3.7e-50)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (b <= 1.15e+232)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.9e+51], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-32], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-127], t$95$1, If[LessEqual[b, -1.6e-176], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e-304], t$95$1, If[LessEqual[b, 1e-147], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-50], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+232], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -2.8999999999999998e51

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.8999999999999998e51 < b < -1.00000000000000006e-32

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.00000000000000006e-32 < b < -2.0000000000000001e-127 or -1.59999999999999992e-176 < b < 4.10000000000000002e-304

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.0000000000000001e-127 < b < -1.59999999999999992e-176

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 4.10000000000000002e-304 < b < 9.9999999999999997e-148

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 42.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 9.9999999999999997e-148 < b < 3.7000000000000001e-50

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 30.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y2 around inf 46.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 3.7000000000000001e-50 < b < 1.15000000000000003e232

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]

   if 1.15000000000000003e232 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 75.3%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 10^{-147}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-50}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+232}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -1.4e+55)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -1.42e-24)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -5e-127)
         t_1
         (if (<= b -3.4e-177)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b 1.12e-270)
             t_1
             (if (<= b 1.45e-50)
               (* y0 (* y2 (- (* x c) (* k y5))))
               (if (<= b 8.4e+231)
                 (* t (* z (- (* c i) (* a b))))
                 (* j (* b (- (* t y4) (* x 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) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.4e+55) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.42e-24) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -5e-127) {
		tmp = t_1;
	} else if (b <= -3.4e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.12e-270) {
		tmp = t_1;
	} else if (b <= 1.45e-50) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (b <= 8.4e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-1.4d+55)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-1.42d-24)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-5d-127)) then
        tmp = t_1
    else if (b <= (-3.4d-177)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 1.12d-270) then
        tmp = t_1
    else if (b <= 1.45d-50) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (b <= 8.4d+231) then
        tmp = t * (z * ((c * i) - (a * b)))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.4e+55) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.42e-24) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -5e-127) {
		tmp = t_1;
	} else if (b <= -3.4e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.12e-270) {
		tmp = t_1;
	} else if (b <= 1.45e-50) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (b <= 8.4e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -1.4e+55:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -1.42e-24:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -5e-127:
		tmp = t_1
	elif b <= -3.4e-177:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 1.12e-270:
		tmp = t_1
	elif b <= 1.45e-50:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif b <= 8.4e+231:
		tmp = t * (z * ((c * i) - (a * b)))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -1.4e+55)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -1.42e-24)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -5e-127)
		tmp = t_1;
	elseif (b <= -3.4e-177)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 1.12e-270)
		tmp = t_1;
	elseif (b <= 1.45e-50)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (b <= 8.4e+231)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -1.4e+55)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -1.42e-24)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -5e-127)
		tmp = t_1;
	elseif (b <= -3.4e-177)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 1.12e-270)
		tmp = t_1;
	elseif (b <= 1.45e-50)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (b <= 8.4e+231)
		tmp = t * (z * ((c * i) - (a * b)));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+55], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.42e-24], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e-127], t$95$1, If[LessEqual[b, -3.4e-177], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e-270], t$95$1, If[LessEqual[b, 1.45e-50], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.4e+231], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.4e55

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.4e55 < b < -1.42e-24

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.42e-24 < b < -4.9999999999999997e-127 or -3.4000000000000001e-177 < b < 1.1199999999999999e-270

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 31.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 31.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 31.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 31.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 31.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 31.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 31.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -4.9999999999999997e-127 < b < -3.4000000000000001e-177

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 1.1199999999999999e-270 < b < 1.45000000000000004e-50

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 38.2%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   if 1.45000000000000004e-50 < b < 8.39999999999999937e231

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]

   if 8.39999999999999937e231 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 75.3%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-127}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;a \leq -0.0001:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-136}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(z \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (* z t))))))
   (if (<= a -0.0001)
     t_1
     (if (<= a -2.8e-90)
       (* i (* j (* x y1)))
       (if (<= a -8e-136)
         (* y0 (* y3 (* z (- c))))
         (if (<= a -1.5e-222)
           (* c (* y (* y3 y4)))
           (if (<= a -3.8e-262)
             (* (- j) (* y1 (* y3 y4)))
             (if (<= a 1.5e+183) (* b (* j (- (* t y4) (* x y0)))) 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) - (z * t)));
	double tmp;
	if (a <= -0.0001) {
		tmp = t_1;
	} else if (a <= -2.8e-90) {
		tmp = i * (j * (x * y1));
	} else if (a <= -8e-136) {
		tmp = y0 * (y3 * (z * -c));
	} else if (a <= -1.5e-222) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= -3.8e-262) {
		tmp = -j * (y1 * (y3 * y4));
	} else if (a <= 1.5e+183) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} 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) - (z * t)))
    if (a <= (-0.0001d0)) then
        tmp = t_1
    else if (a <= (-2.8d-90)) then
        tmp = i * (j * (x * y1))
    else if (a <= (-8d-136)) then
        tmp = y0 * (y3 * (z * -c))
    else if (a <= (-1.5d-222)) then
        tmp = c * (y * (y3 * y4))
    else if (a <= (-3.8d-262)) then
        tmp = -j * (y1 * (y3 * y4))
    else if (a <= 1.5d+183) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    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) - (z * t)));
	double tmp;
	if (a <= -0.0001) {
		tmp = t_1;
	} else if (a <= -2.8e-90) {
		tmp = i * (j * (x * y1));
	} else if (a <= -8e-136) {
		tmp = y0 * (y3 * (z * -c));
	} else if (a <= -1.5e-222) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= -3.8e-262) {
		tmp = -j * (y1 * (y3 * y4));
	} else if (a <= 1.5e+183) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} 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) - (z * t)))
	tmp = 0
	if a <= -0.0001:
		tmp = t_1
	elif a <= -2.8e-90:
		tmp = i * (j * (x * y1))
	elif a <= -8e-136:
		tmp = y0 * (y3 * (z * -c))
	elif a <= -1.5e-222:
		tmp = c * (y * (y3 * y4))
	elif a <= -3.8e-262:
		tmp = -j * (y1 * (y3 * y4))
	elif a <= 1.5e+183:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (a <= -0.0001)
		tmp = t_1;
	elseif (a <= -2.8e-90)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (a <= -8e-136)
		tmp = Float64(y0 * Float64(y3 * Float64(z * Float64(-c))));
	elseif (a <= -1.5e-222)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (a <= -3.8e-262)
		tmp = Float64(Float64(-j) * Float64(y1 * Float64(y3 * y4)));
	elseif (a <= 1.5e+183)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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) - (z * t)));
	tmp = 0.0;
	if (a <= -0.0001)
		tmp = t_1;
	elseif (a <= -2.8e-90)
		tmp = i * (j * (x * y1));
	elseif (a <= -8e-136)
		tmp = y0 * (y3 * (z * -c));
	elseif (a <= -1.5e-222)
		tmp = c * (y * (y3 * y4));
	elseif (a <= -3.8e-262)
		tmp = -j * (y1 * (y3 * y4));
	elseif (a <= 1.5e+183)
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0001], t$95$1, If[LessEqual[a, -2.8e-90], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e-136], N[(y0 * N[(y3 * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-222], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-262], N[((-j) * N[(y1 * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+183], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.00000000000000005e-4 or 1.49999999999999998e183 < a

   1. Initial program 20.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.00000000000000005e-4 < a < -2.7999999999999999e-90

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 33.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 33.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 33.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 33.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 35.0%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 50.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 50.9%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -2.7999999999999999e-90 < a < -8.00000000000000001e-136

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 0.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 0.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 0.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 0.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 0.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 0.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 0.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 0.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 0.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 40.7%

      \[\leadsto y0 \cdot \color{blue}{\left(-1 \cdot \left(y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.7%

         \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   8. Simplified 40.7%

      \[\leadsto y0 \cdot \color{blue}{\left(-y3 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   9. Taylor expanded in c around inf 41.5%

      \[\leadsto y0 \cdot \left(-y3 \cdot \color{blue}{\left(c \cdot z\right)}\right) \]

   if -8.00000000000000001e-136 < a < -1.50000000000000015e-222

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 23.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 23.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 23.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 23.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 23.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 23.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 23.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 54.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 32.1%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 32.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 32.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 32.1%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 32.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 48.5%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -1.50000000000000015e-222 < a < -3.8000000000000002e-262

   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. Add Preprocessing

   3. Taylor expanded in y around inf 28.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 28.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 28.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 28.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 28.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 28.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 28.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 37.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

      2. neg-mul-1 46.4%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right) \]

      3. *-commutative 46.4%

         \[\leadsto \left(-j\right) \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   9. Simplified 46.4%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if -3.8000000000000002e-262 < a < 1.49999999999999998e183

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 43.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0001:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-136}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(z \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-262}:\\ \;\;\;\;\left(-j\right) \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 370000000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= b -1.9e+51)
     (* a (* b (- (* x y) (* z t))))
     (if (<= b -1.85e-29)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= b -4.3e-126)
         t_1
         (if (<= b -4.2e-177)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b 3.2e-307)
             t_1
             (if (<= b 370000000000.0)
               (* i (* y1 (- (* x j) (* z k))))
               (* j (* b (- (* t y4) (* x 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) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.9e+51) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.85e-29) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -4.3e-126) {
		tmp = t_1;
	} else if (b <= -4.2e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 3.2e-307) {
		tmp = t_1;
	} else if (b <= 370000000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	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 * (y0 * ((x * y2) - (z * y3)))
    if (b <= (-1.9d+51)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-1.85d-29)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (b <= (-4.3d-126)) then
        tmp = t_1
    else if (b <= (-4.2d-177)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 3.2d-307) then
        tmp = t_1
    else if (b <= 370000000000.0d0) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else
        tmp = j * (b * ((t * y4) - (x * y0)))
    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 * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (b <= -1.9e+51) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -1.85e-29) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (b <= -4.3e-126) {
		tmp = t_1;
	} else if (b <= -4.2e-177) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 3.2e-307) {
		tmp = t_1;
	} else if (b <= 370000000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else {
		tmp = j * (b * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if b <= -1.9e+51:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -1.85e-29:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif b <= -4.3e-126:
		tmp = t_1
	elif b <= -4.2e-177:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 3.2e-307:
		tmp = t_1
	elif b <= 370000000000.0:
		tmp = i * (y1 * ((x * j) - (z * k)))
	else:
		tmp = j * (b * ((t * y4) - (x * y0)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (b <= -1.9e+51)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -1.85e-29)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (b <= -4.3e-126)
		tmp = t_1;
	elseif (b <= -4.2e-177)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 3.2e-307)
		tmp = t_1;
	elseif (b <= 370000000000.0)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	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 * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (b <= -1.9e+51)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -1.85e-29)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (b <= -4.3e-126)
		tmp = t_1;
	elseif (b <= -4.2e-177)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 3.2e-307)
		tmp = t_1;
	elseif (b <= 370000000000.0)
		tmp = i * (y1 * ((x * j) - (z * k)));
	else
		tmp = j * (b * ((t * y4) - (x * y0)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+51], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.85e-29], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.3e-126], t$95$1, If[LessEqual[b, -4.2e-177], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-307], t$95$1, If[LessEqual[b, 370000000000.0], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.8999999999999999e51

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.8999999999999999e51 < b < -1.8499999999999999e-29

   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. Add Preprocessing

   3. Taylor expanded in j around inf 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 52.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.8499999999999999e-29 < b < -4.30000000000000033e-126 or -4.20000000000000002e-177 < b < 3.20000000000000011e-307

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 32.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 32.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 32.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -4.30000000000000033e-126 < b < -4.20000000000000002e-177

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 3.20000000000000011e-307 < b < 3.7e11

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 36.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 3.7e11 < b

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 51.1%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 370000000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-140}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right) - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* b (- (* t y4) (* x y0))))))
   (if (<= b -3.6e+105)
     t_1
     (if (<= b -1.1e-140)
       (* y4 (- (* c (- (* y y3) (* t y2))) (* j (* y1 y3))))
       (if (<= b 6e-233)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= b 7.5e-145)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= b 1.45e-50)
             (* y1 (* y4 (- (* k y2) (* j y3))))
             (if (<= b 1.08e+231) (* t (* z (- (* c i) (* a b)))) 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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -3.6e+105) {
		tmp = t_1;
	} else if (b <= -1.1e-140) {
		tmp = y4 * ((c * ((y * y3) - (t * y2))) - (j * (y1 * y3)));
	} else if (b <= 6e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 7.5e-145) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.45e-50) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 1.08e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
    if (b <= (-3.6d+105)) then
        tmp = t_1
    else if (b <= (-1.1d-140)) then
        tmp = y4 * ((c * ((y * y3) - (t * y2))) - (j * (y1 * y3)))
    else if (b <= 6d-233) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (b <= 7.5d-145) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (b <= 1.45d-50) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (b <= 1.08d+231) then
        tmp = t * (z * ((c * i) - (a * b)))
    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 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -3.6e+105) {
		tmp = t_1;
	} else if (b <= -1.1e-140) {
		tmp = y4 * ((c * ((y * y3) - (t * y2))) - (j * (y1 * y3)));
	} else if (b <= 6e-233) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (b <= 7.5e-145) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (b <= 1.45e-50) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (b <= 1.08e+231) {
		tmp = t * (z * ((c * i) - (a * b)));
	} 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 = j * (b * ((t * y4) - (x * y0)))
	tmp = 0
	if b <= -3.6e+105:
		tmp = t_1
	elif b <= -1.1e-140:
		tmp = y4 * ((c * ((y * y3) - (t * y2))) - (j * (y1 * y3)))
	elif b <= 6e-233:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif b <= 7.5e-145:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif b <= 1.45e-50:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif b <= 1.08e+231:
		tmp = t * (z * ((c * i) - (a * b)))
	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(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -3.6e+105)
		tmp = t_1;
	elseif (b <= -1.1e-140)
		tmp = Float64(y4 * Float64(Float64(c * Float64(Float64(y * y3) - Float64(t * y2))) - Float64(j * Float64(y1 * y3))));
	elseif (b <= 6e-233)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (b <= 7.5e-145)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (b <= 1.45e-50)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (b <= 1.08e+231)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	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 = j * (b * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (b <= -3.6e+105)
		tmp = t_1;
	elseif (b <= -1.1e-140)
		tmp = y4 * ((c * ((y * y3) - (t * y2))) - (j * (y1 * y3)));
	elseif (b <= 6e-233)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (b <= 7.5e-145)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (b <= 1.45e-50)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (b <= 1.08e+231)
		tmp = t * (z * ((c * i) - (a * b)));
	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[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+105], t$95$1, If[LessEqual[b, -1.1e-140], N[(y4 * N[(N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-233], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-145], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-50], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.08e+231], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.5999999999999999e105 or 1.08000000000000001e231 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 47.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 63.5%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.5999999999999999e105 < b < -1.1e-140

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 36.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 36.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 36.9%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 36.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 36.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 36.9%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 36.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 37.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 46.4%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 46.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 46.4%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 46.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -1.1e-140 < b < 5.99999999999999997e-233

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.4%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 49.4%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 49.4%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 43.6%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 5.99999999999999997e-233 < b < 7.4999999999999996e-145

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 23.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 7.4999999999999996e-145 < b < 1.45000000000000004e-50

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 54.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 54.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 60.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 1.45000000000000004e-50 < b < 1.08000000000000001e231

   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. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)}\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 41.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right)} - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot j} - z \cdot \left(a \cdot b - c \cdot i\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.5%

         \[\leadsto t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y2}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot j - z \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-140}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right) - j \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-233}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+231}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+280}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -53000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* a b) (* z (- t)))))
   (if (<= a -2.9e+280)
     (* a (* t (* y2 y5)))
     (if (<= a -53000000000.0)
       t_1
       (if (<= a -5.4e-225)
         (* c (* y (* y3 y4)))
         (if (<= a 1.06e-237)
           (* j (* y1 (* x i)))
           (if (<= a 1.15e-121)
             (* j (* y3 (* y0 y5)))
             (if (<= a 4e+35) (* j (* x (* i 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 * b) * (z * -t);
	double tmp;
	if (a <= -2.9e+280) {
		tmp = a * (t * (y2 * y5));
	} else if (a <= -53000000000.0) {
		tmp = t_1;
	} else if (a <= -5.4e-225) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 1.06e-237) {
		tmp = j * (y1 * (x * i));
	} else if (a <= 1.15e-121) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 4e+35) {
		tmp = j * (x * (i * 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 * b) * (z * -t)
    if (a <= (-2.9d+280)) then
        tmp = a * (t * (y2 * y5))
    else if (a <= (-53000000000.0d0)) then
        tmp = t_1
    else if (a <= (-5.4d-225)) then
        tmp = c * (y * (y3 * y4))
    else if (a <= 1.06d-237) then
        tmp = j * (y1 * (x * i))
    else if (a <= 1.15d-121) then
        tmp = j * (y3 * (y0 * y5))
    else if (a <= 4d+35) then
        tmp = j * (x * (i * 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 * b) * (z * -t);
	double tmp;
	if (a <= -2.9e+280) {
		tmp = a * (t * (y2 * y5));
	} else if (a <= -53000000000.0) {
		tmp = t_1;
	} else if (a <= -5.4e-225) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 1.06e-237) {
		tmp = j * (y1 * (x * i));
	} else if (a <= 1.15e-121) {
		tmp = j * (y3 * (y0 * y5));
	} else if (a <= 4e+35) {
		tmp = j * (x * (i * 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 * b) * (z * -t)
	tmp = 0
	if a <= -2.9e+280:
		tmp = a * (t * (y2 * y5))
	elif a <= -53000000000.0:
		tmp = t_1
	elif a <= -5.4e-225:
		tmp = c * (y * (y3 * y4))
	elif a <= 1.06e-237:
		tmp = j * (y1 * (x * i))
	elif a <= 1.15e-121:
		tmp = j * (y3 * (y0 * y5))
	elif a <= 4e+35:
		tmp = j * (x * (i * 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(Float64(a * b) * Float64(z * Float64(-t)))
	tmp = 0.0
	if (a <= -2.9e+280)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (a <= -53000000000.0)
		tmp = t_1;
	elseif (a <= -5.4e-225)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (a <= 1.06e-237)
		tmp = Float64(j * Float64(y1 * Float64(x * i)));
	elseif (a <= 1.15e-121)
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	elseif (a <= 4e+35)
		tmp = Float64(j * Float64(x * Float64(i * 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 * b) * (z * -t);
	tmp = 0.0;
	if (a <= -2.9e+280)
		tmp = a * (t * (y2 * y5));
	elseif (a <= -53000000000.0)
		tmp = t_1;
	elseif (a <= -5.4e-225)
		tmp = c * (y * (y3 * y4));
	elseif (a <= 1.06e-237)
		tmp = j * (y1 * (x * i));
	elseif (a <= 1.15e-121)
		tmp = j * (y3 * (y0 * y5));
	elseif (a <= 4e+35)
		tmp = j * (x * (i * 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[(N[(a * b), $MachinePrecision] * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+280], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -53000000000.0], t$95$1, If[LessEqual[a, -5.4e-225], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e-237], N[(j * N[(y1 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-121], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+35], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.89999999999999985e280

   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. Add Preprocessing

   3. Taylor expanded in y around inf 25.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 25.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 25.0%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 25.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 25.0%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 25.0%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 25.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 76.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 76.1%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 76.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.89999999999999985e280 < a < -5.3e10 or 3.9999999999999999e35 < a

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   5. Taylor expanded in x around 0 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]

      2. associate-*r* 39.0%

         \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

   7. Simplified 39.0%

      \[\leadsto \color{blue}{-\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

   if -5.3e10 < a < -5.39999999999999984e-225

   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. Add Preprocessing

   3. Taylor expanded in y around inf 26.7%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 26.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 26.7%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 26.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 26.7%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 26.7%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 26.7%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 35.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 27.4%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 27.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 27.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 27.4%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 27.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 28.3%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -5.39999999999999984e-225 < a < 1.05999999999999994e-237

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 57.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 57.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 57.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 57.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 31.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 28.4%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto j \cdot \color{blue}{\left(\left(i \cdot x\right) \cdot y1\right)} \]

   9. Simplified 31.6%

      \[\leadsto j \cdot \color{blue}{\left(\left(i \cdot x\right) \cdot y1\right)} \]

   if 1.05999999999999994e-237 < a < 1.15000000000000006e-121

   1. Initial program 45.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 51.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 51.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 51.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 51.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 51.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in y3 around inf 35.4%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   7. Taylor expanded in y0 around inf 32.7%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 32.7%

         \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \]

   9. Simplified 32.7%

      \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot y0\right)}\right) \]

   if 1.15000000000000006e-121 < a < 3.9999999999999999e35

   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. Add Preprocessing

   3. Taylor expanded in j around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 43.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 43.6%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y1 \cdot i\right)}\right) \]

   9. Simplified 43.6%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y1 \cdot i\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+280}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -53000000000:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(z \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_3 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -68000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (* a (* b (- (* x y) (* z t)))))
        (t_3 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= a -2e+194)
     t_2
     (if (<= a -8.8e+96)
       t_1
       (if (<= a -68000000.0)
         t_3
         (if (<= a -5e-262) t_1 (if (<= a 1.5e+183) t_3 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 * (y0 * ((x * y2) - (z * y3)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double t_3 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (a <= -2e+194) {
		tmp = t_2;
	} else if (a <= -8.8e+96) {
		tmp = t_1;
	} else if (a <= -68000000.0) {
		tmp = t_3;
	} else if (a <= -5e-262) {
		tmp = t_1;
	} else if (a <= 1.5e+183) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = a * (b * ((x * y) - (z * t)))
    t_3 = b * (j * ((t * y4) - (x * y0)))
    if (a <= (-2d+194)) then
        tmp = t_2
    else if (a <= (-8.8d+96)) then
        tmp = t_1
    else if (a <= (-68000000.0d0)) then
        tmp = t_3
    else if (a <= (-5d-262)) then
        tmp = t_1
    else if (a <= 1.5d+183) then
        tmp = t_3
    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 * (y0 * ((x * y2) - (z * y3)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double t_3 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (a <= -2e+194) {
		tmp = t_2;
	} else if (a <= -8.8e+96) {
		tmp = t_1;
	} else if (a <= -68000000.0) {
		tmp = t_3;
	} else if (a <= -5e-262) {
		tmp = t_1;
	} else if (a <= 1.5e+183) {
		tmp = t_3;
	} 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 * (y0 * ((x * y2) - (z * y3)))
	t_2 = a * (b * ((x * y) - (z * t)))
	t_3 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if a <= -2e+194:
		tmp = t_2
	elif a <= -8.8e+96:
		tmp = t_1
	elif a <= -68000000.0:
		tmp = t_3
	elif a <= -5e-262:
		tmp = t_1
	elif a <= 1.5e+183:
		tmp = t_3
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_3 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (a <= -2e+194)
		tmp = t_2;
	elseif (a <= -8.8e+96)
		tmp = t_1;
	elseif (a <= -68000000.0)
		tmp = t_3;
	elseif (a <= -5e-262)
		tmp = t_1;
	elseif (a <= 1.5e+183)
		tmp = t_3;
	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 * (y0 * ((x * y2) - (z * y3)));
	t_2 = a * (b * ((x * y) - (z * t)));
	t_3 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (a <= -2e+194)
		tmp = t_2;
	elseif (a <= -8.8e+96)
		tmp = t_1;
	elseif (a <= -68000000.0)
		tmp = t_3;
	elseif (a <= -5e-262)
		tmp = t_1;
	elseif (a <= 1.5e+183)
		tmp = t_3;
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+194], t$95$2, If[LessEqual[a, -8.8e+96], t$95$1, If[LessEqual[a, -68000000.0], t$95$3, If[LessEqual[a, -5e-262], t$95$1, If[LessEqual[a, 1.5e+183], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.99999999999999989e194 or 1.49999999999999998e183 < a

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 61.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.99999999999999989e194 < a < -8.7999999999999996e96 or -6.8e7 < a < -4.99999999999999992e-262

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 34.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 34.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 34.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 34.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 34.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 34.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 34.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 37.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -8.7999999999999996e96 < a < -6.8e7 or -4.99999999999999992e-262 < a < 1.49999999999999998e183

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 40.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 37.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{+96}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -68000000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -0.058:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t)))))
        (t_2 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= a -6.2e+194)
     t_1
     (if (<= a -1.75e+90)
       (* c (* y0 (- (* x y2) (* z y3))))
       (if (<= a -0.058)
         t_2
         (if (<= a -9e-307)
           (* i (* y1 (- (* x j) (* z k))))
           (if (<= a 1.5e+183) 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 * (b * ((x * y) - (z * t)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (a <= -6.2e+194) {
		tmp = t_1;
	} else if (a <= -1.75e+90) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -0.058) {
		tmp = t_2;
	} else if (a <= -9e-307) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 1.5e+183) {
		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 * (b * ((x * y) - (z * t)))
    t_2 = b * (j * ((t * y4) - (x * y0)))
    if (a <= (-6.2d+194)) then
        tmp = t_1
    else if (a <= (-1.75d+90)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (a <= (-0.058d0)) then
        tmp = t_2
    else if (a <= (-9d-307)) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (a <= 1.5d+183) 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 * (b * ((x * y) - (z * t)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (a <= -6.2e+194) {
		tmp = t_1;
	} else if (a <= -1.75e+90) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= -0.058) {
		tmp = t_2;
	} else if (a <= -9e-307) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (a <= 1.5e+183) {
		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 * (b * ((x * y) - (z * t)))
	t_2 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if a <= -6.2e+194:
		tmp = t_1
	elif a <= -1.75e+90:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif a <= -0.058:
		tmp = t_2
	elif a <= -9e-307:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif a <= 1.5e+183:
		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(b * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (a <= -6.2e+194)
		tmp = t_1;
	elseif (a <= -1.75e+90)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (a <= -0.058)
		tmp = t_2;
	elseif (a <= -9e-307)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (a <= 1.5e+183)
		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 * (b * ((x * y) - (z * t)));
	t_2 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (a <= -6.2e+194)
		tmp = t_1;
	elseif (a <= -1.75e+90)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (a <= -0.058)
		tmp = t_2;
	elseif (a <= -9e-307)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (a <= 1.5e+183)
		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[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+194], t$95$1, If[LessEqual[a, -1.75e+90], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.058], t$95$2, If[LessEqual[a, -9e-307], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+183], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.1999999999999999e194 or 1.49999999999999998e183 < a

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 61.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -6.1999999999999999e194 < a < -1.7499999999999999e90

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 41.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 41.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 41.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 41.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 41.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 41.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 42.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.7499999999999999e90 < a < -0.0580000000000000029 or -8.99999999999999978e-307 < a < 1.49999999999999998e183

   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. Add Preprocessing

   3. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 41.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 41.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 41.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -0.0580000000000000029 < a < -8.99999999999999978e-307

   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. Add Preprocessing

   3. Taylor expanded in y1 around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 36.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 36.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 38.3%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -0.058:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 32.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := t \cdot y4 - x \cdot y0\\ t_3 := j \cdot \left(b \cdot t\_2\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(j \cdot t\_2\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 11500000000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (- (* t y4) (* x y0)))
        (t_3 (* j (* b t_2))))
   (if (<= b -6.8e+92)
     t_3
     (if (<= b -1.25e-125)
       t_1
       (if (<= b -2.7e-161)
         (* b (* j t_2))
         (if (<= b 1.2e-303)
           t_1
           (if (<= b 11500000000000.0)
             (* i (* y1 (- (* x j) (* z k))))
             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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = (t * y4) - (x * y0);
	double t_3 = j * (b * t_2);
	double tmp;
	if (b <= -6.8e+92) {
		tmp = t_3;
	} else if (b <= -1.25e-125) {
		tmp = t_1;
	} else if (b <= -2.7e-161) {
		tmp = b * (j * t_2);
	} else if (b <= 1.2e-303) {
		tmp = t_1;
	} else if (b <= 11500000000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} 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 = c * (y0 * ((x * y2) - (z * y3)))
    t_2 = (t * y4) - (x * y0)
    t_3 = j * (b * t_2)
    if (b <= (-6.8d+92)) then
        tmp = t_3
    else if (b <= (-1.25d-125)) then
        tmp = t_1
    else if (b <= (-2.7d-161)) then
        tmp = b * (j * t_2)
    else if (b <= 1.2d-303) then
        tmp = t_1
    else if (b <= 11500000000000.0d0) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    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 = c * (y0 * ((x * y2) - (z * y3)));
	double t_2 = (t * y4) - (x * y0);
	double t_3 = j * (b * t_2);
	double tmp;
	if (b <= -6.8e+92) {
		tmp = t_3;
	} else if (b <= -1.25e-125) {
		tmp = t_1;
	} else if (b <= -2.7e-161) {
		tmp = b * (j * t_2);
	} else if (b <= 1.2e-303) {
		tmp = t_1;
	} else if (b <= 11500000000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} 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 = c * (y0 * ((x * y2) - (z * y3)))
	t_2 = (t * y4) - (x * y0)
	t_3 = j * (b * t_2)
	tmp = 0
	if b <= -6.8e+92:
		tmp = t_3
	elif b <= -1.25e-125:
		tmp = t_1
	elif b <= -2.7e-161:
		tmp = b * (j * t_2)
	elif b <= 1.2e-303:
		tmp = t_1
	elif b <= 11500000000000.0:
		tmp = i * (y1 * ((x * j) - (z * k)))
	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(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(Float64(t * y4) - Float64(x * y0))
	t_3 = Float64(j * Float64(b * t_2))
	tmp = 0.0
	if (b <= -6.8e+92)
		tmp = t_3;
	elseif (b <= -1.25e-125)
		tmp = t_1;
	elseif (b <= -2.7e-161)
		tmp = Float64(b * Float64(j * t_2));
	elseif (b <= 1.2e-303)
		tmp = t_1;
	elseif (b <= 11500000000000.0)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	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 = c * (y0 * ((x * y2) - (z * y3)));
	t_2 = (t * y4) - (x * y0);
	t_3 = j * (b * t_2);
	tmp = 0.0;
	if (b <= -6.8e+92)
		tmp = t_3;
	elseif (b <= -1.25e-125)
		tmp = t_1;
	elseif (b <= -2.7e-161)
		tmp = b * (j * t_2);
	elseif (b <= 1.2e-303)
		tmp = t_1;
	elseif (b <= 11500000000000.0)
		tmp = i * (y1 * ((x * j) - (z * k)));
	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[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+92], t$95$3, If[LessEqual[b, -1.25e-125], t$95$1, If[LessEqual[b, -2.7e-161], N[(b * N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-303], t$95$1, If[LessEqual[b, 11500000000000.0], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.7999999999999996e92 or 1.15e13 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 51.4%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -6.7999999999999996e92 < b < -1.24999999999999992e-125 or -2.6999999999999999e-161 < b < 1.2e-303

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 35.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 35.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 35.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 35.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 41.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.24999999999999992e-125 < b < -2.6999999999999999e-161

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 33.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 33.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 33.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 33.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 33.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 1.2e-303 < b < 1.15e13

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 36.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 11500000000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 32.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 56000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3)))))
        (t_2 (* j (* b (- (* t y4) (* x y0))))))
   (if (<= b -3.5e+94)
     t_2
     (if (<= b -2.5e-126)
       t_1
       (if (<= b -5.2e-174)
         (* j (* t (- (* b y4) (* i y5))))
         (if (<= b 2.8e-307)
           t_1
           (if (<= b 56000000.0) (* i (* y1 (- (* x j) (* z k)))) 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 * (y0 * ((x * y2) - (z * y3)));
	double t_2 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -3.5e+94) {
		tmp = t_2;
	} else if (b <= -2.5e-126) {
		tmp = t_1;
	} else if (b <= -5.2e-174) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 2.8e-307) {
		tmp = t_1;
	} else if (b <= 56000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} 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 * (y0 * ((x * y2) - (z * y3)))
    t_2 = j * (b * ((t * y4) - (x * y0)))
    if (b <= (-3.5d+94)) then
        tmp = t_2
    else if (b <= (-2.5d-126)) then
        tmp = t_1
    else if (b <= (-5.2d-174)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 2.8d-307) then
        tmp = t_1
    else if (b <= 56000000.0d0) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    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 * (y0 * ((x * y2) - (z * y3)));
	double t_2 = j * (b * ((t * y4) - (x * y0)));
	double tmp;
	if (b <= -3.5e+94) {
		tmp = t_2;
	} else if (b <= -2.5e-126) {
		tmp = t_1;
	} else if (b <= -5.2e-174) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 2.8e-307) {
		tmp = t_1;
	} else if (b <= 56000000.0) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} 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 * (y0 * ((x * y2) - (z * y3)))
	t_2 = j * (b * ((t * y4) - (x * y0)))
	tmp = 0
	if b <= -3.5e+94:
		tmp = t_2
	elif b <= -2.5e-126:
		tmp = t_1
	elif b <= -5.2e-174:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 2.8e-307:
		tmp = t_1
	elif b <= 56000000.0:
		tmp = i * (y1 * ((x * j) - (z * k)))
	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(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	t_2 = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (b <= -3.5e+94)
		tmp = t_2;
	elseif (b <= -2.5e-126)
		tmp = t_1;
	elseif (b <= -5.2e-174)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 2.8e-307)
		tmp = t_1;
	elseif (b <= 56000000.0)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	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 * (y0 * ((x * y2) - (z * y3)));
	t_2 = j * (b * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (b <= -3.5e+94)
		tmp = t_2;
	elseif (b <= -2.5e-126)
		tmp = t_1;
	elseif (b <= -5.2e-174)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 2.8e-307)
		tmp = t_1;
	elseif (b <= 56000000.0)
		tmp = i * (y1 * ((x * j) - (z * k)));
	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[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+94], t$95$2, If[LessEqual[b, -2.5e-126], t$95$1, If[LessEqual[b, -5.2e-174], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-307], t$95$1, If[LessEqual[b, 56000000.0], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4999999999999997e94 or 5.6e7 < b

   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. Add Preprocessing

   3. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 51.4%

      \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.4999999999999997e94 < b < -2.50000000000000003e-126 or -5.2000000000000004e-174 < b < 2.8e-307

   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. Add Preprocessing

   3. Taylor expanded in y0 around inf 35.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 35.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 35.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 35.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 35.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 35.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 35.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 35.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 35.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.50000000000000003e-126 < b < -5.2000000000000004e-174

   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. Add Preprocessing

   3. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 43.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 43.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 2.8e-307 < b < 5.6e7

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 36.7%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 56000000:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -4.5 \cdot 10^{+144}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3600000000000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+175}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -4.5e+144)
   (* y4 (* c (* y y3)))
   (if (<= y3 -3.5e-186)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y3 3600000000000.0)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y3 2.7e+137)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y3 7.8e+175)
           (* c (* y (* y3 y4)))
           (* j (* y0 (* 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 tmp;
	if (y3 <= -4.5e+144) {
		tmp = y4 * (c * (y * y3));
	} else if (y3 <= -3.5e-186) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 3600000000000.0) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y3 <= 2.7e+137) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 7.8e+175) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y0 * (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) :: tmp
    if (y3 <= (-4.5d+144)) then
        tmp = y4 * (c * (y * y3))
    else if (y3 <= (-3.5d-186)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y3 <= 3600000000000.0d0) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y3 <= 2.7d+137) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y3 <= 7.8d+175) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = j * (y0 * (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 tmp;
	if (y3 <= -4.5e+144) {
		tmp = y4 * (c * (y * y3));
	} else if (y3 <= -3.5e-186) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y3 <= 3600000000000.0) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y3 <= 2.7e+137) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 7.8e+175) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -4.5e+144:
		tmp = y4 * (c * (y * y3))
	elif y3 <= -3.5e-186:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y3 <= 3600000000000.0:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y3 <= 2.7e+137:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y3 <= 7.8e+175:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	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 (y3 <= -4.5e+144)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y3 <= -3.5e-186)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y3 <= 3600000000000.0)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y3 <= 2.7e+137)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 7.8e+175)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(j * Float64(y0 * 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)
	tmp = 0.0;
	if (y3 <= -4.5e+144)
		tmp = y4 * (c * (y * y3));
	elseif (y3 <= -3.5e-186)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y3 <= 3600000000000.0)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y3 <= 2.7e+137)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y3 <= 7.8e+175)
		tmp = c * (y * (y3 * y4));
	else
		tmp = j * (y0 * (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_] := If[LessEqual[y3, -4.5e+144], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.5e-186], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3600000000000.0], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.7e+137], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.8e+175], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -4.49999999999999967e144

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 35.4%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 35.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 35.4%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 35.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 35.4%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 35.4%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 35.4%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 55.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 55.1%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 55.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 50.1%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 50.1%

          \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y3 \cdot y\right)}\right) \]

   12. Simplified 50.1%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]

   if -4.49999999999999967e144 < y3 < -3.49999999999999989e-186

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in x around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -3.49999999999999989e-186 < y3 < 3.6e12

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 42.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in b around inf 37.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.6e12 < y3 < 2.70000000000000017e137

   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. Add Preprocessing

   3. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 2.70000000000000017e137 < y3 < 7.79999999999999944e175

   1. Initial program 10.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 19.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 19.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 19.8%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 19.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 19.8%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 19.8%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 19.8%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 37.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 38.3%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 38.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 38.3%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 38.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 55.4%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 7.79999999999999944e175 < y3

   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. Add Preprocessing

   3. Taylor expanded in y around inf 44.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.9%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 44.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 38.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y0 around inf 42.1%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.5 \cdot 10^{+144}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 3600000000000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 2.7 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+175}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{if}\;y2 \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{-141}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{+165}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* t (* y2 y5)))))
   (if (<= y2 -2.3e-22)
     t_1
     (if (<= y2 9.5e-141)
       (* j (* x (* i y1)))
       (if (<= y2 2.5e+165) (* c (* y (* y3 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 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -2.3e-22) {
		tmp = t_1;
	} else if (y2 <= 9.5e-141) {
		tmp = j * (x * (i * y1));
	} else if (y2 <= 2.5e+165) {
		tmp = c * (y * (y3 * 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 = a * (t * (y2 * y5))
    if (y2 <= (-2.3d-22)) then
        tmp = t_1
    else if (y2 <= 9.5d-141) then
        tmp = j * (x * (i * y1))
    else if (y2 <= 2.5d+165) then
        tmp = c * (y * (y3 * 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 = a * (t * (y2 * y5));
	double tmp;
	if (y2 <= -2.3e-22) {
		tmp = t_1;
	} else if (y2 <= 9.5e-141) {
		tmp = j * (x * (i * y1));
	} else if (y2 <= 2.5e+165) {
		tmp = c * (y * (y3 * 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 = a * (t * (y2 * y5))
	tmp = 0
	if y2 <= -2.3e-22:
		tmp = t_1
	elif y2 <= 9.5e-141:
		tmp = j * (x * (i * y1))
	elif y2 <= 2.5e+165:
		tmp = c * (y * (y3 * 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(a * Float64(t * Float64(y2 * y5)))
	tmp = 0.0
	if (y2 <= -2.3e-22)
		tmp = t_1;
	elseif (y2 <= 9.5e-141)
		tmp = Float64(j * Float64(x * Float64(i * y1)));
	elseif (y2 <= 2.5e+165)
		tmp = Float64(c * Float64(y * Float64(y3 * 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 = a * (t * (y2 * y5));
	tmp = 0.0;
	if (y2 <= -2.3e-22)
		tmp = t_1;
	elseif (y2 <= 9.5e-141)
		tmp = j * (x * (i * y1));
	elseif (y2 <= 2.5e+165)
		tmp = c * (y * (y3 * 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[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.3e-22], t$95$1, If[LessEqual[y2, 9.5e-141], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.5e+165], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.2999999999999998e-22 or 2.49999999999999985e165 < y2

   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. Add Preprocessing

   3. Taylor expanded in y around inf 30.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 30.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 30.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 30.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 30.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 30.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 30.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 42.9%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.2999999999999998e-22 < y2 < 9.49999999999999996e-141

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 44.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 35.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 28.1%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y1 \cdot i\right)}\right) \]

   9. Simplified 28.1%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(y1 \cdot i\right)}\right) \]

   if 9.49999999999999996e-141 < y2 < 2.49999999999999985e165

   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. Add Preprocessing

   3. Taylor expanded in y around inf 39.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 39.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 39.0%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 39.0%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 39.0%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 39.0%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 39.0%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 37.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 36.0%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 36.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 36.0%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 36.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 27.3%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.3 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{-141}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{+165}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (* y y3)))))
   (if (<= y -6.1e+121)
     t_1
     (if (<= y -3.25e-305)
       (* j (* y1 (* x i)))
       (if (<= y 9e+132) (* a (* t (* y2 y5))) 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 * (c * (y * y3));
	double tmp;
	if (y <= -6.1e+121) {
		tmp = t_1;
	} else if (y <= -3.25e-305) {
		tmp = j * (y1 * (x * i));
	} else if (y <= 9e+132) {
		tmp = a * (t * (y2 * y5));
	} 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 * (c * (y * y3))
    if (y <= (-6.1d+121)) then
        tmp = t_1
    else if (y <= (-3.25d-305)) then
        tmp = j * (y1 * (x * i))
    else if (y <= 9d+132) then
        tmp = a * (t * (y2 * y5))
    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 * (c * (y * y3));
	double tmp;
	if (y <= -6.1e+121) {
		tmp = t_1;
	} else if (y <= -3.25e-305) {
		tmp = j * (y1 * (x * i));
	} else if (y <= 9e+132) {
		tmp = a * (t * (y2 * y5));
	} 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 * (c * (y * y3))
	tmp = 0
	if y <= -6.1e+121:
		tmp = t_1
	elif y <= -3.25e-305:
		tmp = j * (y1 * (x * i))
	elif y <= 9e+132:
		tmp = a * (t * (y2 * y5))
	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(c * Float64(y * y3)))
	tmp = 0.0
	if (y <= -6.1e+121)
		tmp = t_1;
	elseif (y <= -3.25e-305)
		tmp = Float64(j * Float64(y1 * Float64(x * i)));
	elseif (y <= 9e+132)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	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 * (c * (y * y3));
	tmp = 0.0;
	if (y <= -6.1e+121)
		tmp = t_1;
	elseif (y <= -3.25e-305)
		tmp = j * (y1 * (x * i));
	elseif (y <= 9e+132)
		tmp = a * (t * (y2 * y5));
	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[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.1e+121], t$95$1, If[LessEqual[y, -3.25e-305], N[(j * N[(y1 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+132], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0999999999999998e121 or 8.99999999999999944e132 < y

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 38.3%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 38.3%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 38.3%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 38.3%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 38.3%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 38.3%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 37.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 42.0%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 42.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 42.0%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 42.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 43.7%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 43.7%

          \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y3 \cdot y\right)}\right) \]

   12. Simplified 43.7%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]

   if -6.0999999999999998e121 < y < -3.24999999999999996e-305

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 44.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 36.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 26.8%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.8%

         \[\leadsto j \cdot \color{blue}{\left(\left(i \cdot x\right) \cdot y1\right)} \]

   9. Simplified 28.8%

      \[\leadsto j \cdot \color{blue}{\left(\left(i \cdot x\right) \cdot y1\right)} \]

   if -3.24999999999999996e-305 < y < 8.99999999999999944e132

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 34.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 34.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.6%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.6%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.6%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.6%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 36.0%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 27.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 27.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+121}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 24.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -4.2 \cdot 10^{+194}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -4.2e+194)
   (* (- c) (* t (* y2 y4)))
   (if (<= y4 -4.4e-284)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y4 6e+52) (* i (* j (* x y1))) (* c (* y (* y3 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 <= -4.2e+194) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= -4.4e-284) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 6e+52) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (y * (y3 * 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 <= (-4.2d+194)) then
        tmp = -c * (t * (y2 * y4))
    else if (y4 <= (-4.4d-284)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y4 <= 6d+52) then
        tmp = i * (j * (x * y1))
    else
        tmp = c * (y * (y3 * 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 <= -4.2e+194) {
		tmp = -c * (t * (y2 * y4));
	} else if (y4 <= -4.4e-284) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y4 <= 6e+52) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (y * (y3 * 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 <= -4.2e+194:
		tmp = -c * (t * (y2 * y4))
	elif y4 <= -4.4e-284:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y4 <= 6e+52:
		tmp = i * (j * (x * y1))
	else:
		tmp = c * (y * (y3 * 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 <= -4.2e+194)
		tmp = Float64(Float64(-c) * Float64(t * Float64(y2 * y4)));
	elseif (y4 <= -4.4e-284)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 6e+52)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * 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 <= -4.2e+194)
		tmp = -c * (t * (y2 * y4));
	elseif (y4 <= -4.4e-284)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y4 <= 6e+52)
		tmp = i * (j * (x * y1));
	else
		tmp = c * (y * (y3 * 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, -4.2e+194], N[((-c) * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.4e-284], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e+52], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -4.20000000000000032e194

   1. Initial program 14.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 25.1%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 25.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 25.1%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 25.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 25.1%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 25.1%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 25.1%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 36.3%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(t \cdot \left(y2 \cdot y4\right)\right) \]

      3. *-commutative 50.8%

         \[\leadsto \left(-c\right) \cdot \left(t \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   9. Simplified 50.8%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(t \cdot \left(y4 \cdot y2\right)\right)} \]

   if -4.20000000000000032e194 < y4 < -4.4000000000000001e-284

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in a around inf 39.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -4.4000000000000001e-284 < y4 < 6e52

   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. Add Preprocessing

   3. Taylor expanded in j around inf 47.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   6. Taylor expanded in x around inf 32.9%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   7. Taylor expanded in i around inf 26.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 26.6%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   9. Simplified 26.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 6e52 < y4

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.4%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 31.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 31.4%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 31.4%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 31.4%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 31.4%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 31.4%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 33.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 43.9%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 43.9%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 43.9%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 43.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 42.1%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.2 \cdot 10^{+194}:\\ \;\;\;\;\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-24} \lor \neg \left(y2 \leq 8.2 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -2.9e-24) (not (<= y2 8.2e+138)))
   (* a (* t (* y2 y5)))
   (* a (* (* x y) b))))

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 ((y2 <= -2.9e-24) || !(y2 <= 8.2e+138)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	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 ((y2 <= (-2.9d-24)) .or. (.not. (y2 <= 8.2d+138))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = a * ((x * y) * b)
    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 ((y2 <= -2.9e-24) || !(y2 <= 8.2e+138)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -2.9e-24) or not (y2 <= 8.2e+138):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = a * ((x * y) * b)
	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 ((y2 <= -2.9e-24) || !(y2 <= 8.2e+138))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	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 ((y2 <= -2.9e-24) || ~((y2 <= 8.2e+138)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -2.9e-24], N[Not[LessEqual[y2, 8.2e+138]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -2.8999999999999999e-24 or 8.19999999999999961e138 < y2

   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. Add Preprocessing

   3. Taylor expanded in y around inf 27.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 27.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 27.9%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 27.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 27.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 27.9%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 27.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 41.5%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.8999999999999999e-24 < y2 < 8.19999999999999961e138

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 34.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 34.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.9%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.9%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.9%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 34.9%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 34.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in b around inf 19.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{-24} \lor \neg \left(y2 \leq 8.2 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 21.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.6 \cdot 10^{-21} \lor \neg \left(y2 \leq 2.35 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -1.6e-21) (not (<= y2 2.35e+166)))
   (* a (* t (* y2 y5)))
   (* c (* y (* y3 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 ((y2 <= -1.6e-21) || !(y2 <= 2.35e+166)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = c * (y * (y3 * 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 ((y2 <= (-1.6d-21)) .or. (.not. (y2 <= 2.35d+166))) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = c * (y * (y3 * 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 ((y2 <= -1.6e-21) || !(y2 <= 2.35e+166)) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = c * (y * (y3 * 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 (y2 <= -1.6e-21) or not (y2 <= 2.35e+166):
		tmp = a * (t * (y2 * y5))
	else:
		tmp = c * (y * (y3 * 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 ((y2 <= -1.6e-21) || !(y2 <= 2.35e+166))
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * 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 ((y2 <= -1.6e-21) || ~((y2 <= 2.35e+166)))
		tmp = a * (t * (y2 * y5));
	else
		tmp = c * (y * (y3 * 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[Or[LessEqual[y2, -1.6e-21], N[Not[LessEqual[y2, 2.35e+166]], $MachinePrecision]], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -1.6000000000000001e-21 or 2.35e166 < y2

   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. Add Preprocessing

   3. Taylor expanded in y around inf 30.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 30.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 30.2%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 30.2%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 30.2%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 30.2%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 30.2%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y around 0 42.9%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   7. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.3%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   9. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -1.6000000000000001e-21 < y2 < 2.35e166

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 33.1%

      \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. +-commutative 33.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.1%

         \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 33.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 33.1%

         \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 33.1%

         \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.1%

      \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in k around 0 32.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   7. Taylor expanded in y4 around inf 31.3%

      \[\leadsto \color{blue}{y4 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-1 \cdot j\right) \cdot \left(y1 \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. neg-mul-1 31.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(-j\right)} \cdot \left(y1 \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 31.3%

         \[\leadsto y4 \cdot \left(\left(-j\right) \cdot \color{blue}{\left(y3 \cdot y1\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   9. Simplified 31.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(-j\right) \cdot \left(y3 \cdot y1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   10. Taylor expanded in y around inf 24.2%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.6 \cdot 10^{-21} \lor \neg \left(y2 \leq 2.35 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

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 * ((x * y) * b);
}

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 * ((x * y) * b)
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 * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in y around inf 32.0%

   \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
4. Step-by-step derivation

   1. +-commutative 32.0%

      \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) + -1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. mul-1-neg 32.0%

      \[\leadsto \left(y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(-k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. unsub-neg 32.0%

      \[\leadsto \left(y \cdot \color{blue}{\left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. *-commutative 32.0%

      \[\leadsto \left(y \cdot \left(\color{blue}{\left(a \cdot b - c \cdot i\right) \cdot x} - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. *-commutative 32.0%

      \[\leadsto \left(y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

5. Simplified 32.0%

   \[\leadsto \left(\color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(b \cdot y4 - i \cdot y5\right) \cdot k\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

6. Taylor expanded in k around 0 34.4%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

7. Taylor expanded in b around inf 17.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

8. Final simplification 17.3%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
9. Add Preprocessing

Developer target: 28.0% accurate, 0.7× 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 2024095 
(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

  :alt
  (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)))))