Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.7% → 53.0%

Time: 33.6s

Alternatives: 30

Speedup: 3.6×

• 89.2% 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: 29.7% 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: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := \left(\left(\left(\left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right) + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t\_2 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_1 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot t\_1 - \left(k \cdot t\_2 + x \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 (- (* b y4) (* i y5)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* t_2 (- (* t j) (* y k))))
           (* t_1 (- (* y y3) (* t y2))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))
   (if (<= t_3 INFINITY)
     t_3
     (* y (- (* y3 t_1) (+ (* k t_2) (* x (- (* 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 = (c * y4) - (a * y5);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (t_1 * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y * ((y3 * t_1) - ((k * t_2) + (x * ((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 = (c * y4) - (a * y5);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (t_1 * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y * ((y3 * t_1) - ((k * t_2) + (x * ((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 = (c * y4) - (a * y5)
	t_2 = (b * y4) - (i * y5)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (t_1 * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = y * ((y3 * t_1) - ((k * t_2) + (x * ((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(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_2 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(t_1 * Float64(Float64(y * y3) - Float64(t * y2)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y * Float64(Float64(y3 * t_1) - Float64(Float64(k * t_2) + Float64(x * 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 = (c * y4) - (a * y5);
	t_2 = (b * y4) - (i * y5);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (t_1 * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = y * ((y3 * t_1) - ((k * t_2) + (x * ((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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $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$3, Infinity], t$95$3, N[(y * N[(N[(y3 * t$95$1), $MachinePrecision] - N[(N[(k * t$95$2), $MachinePrecision] + N[(x * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.0%

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

   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 y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot k + \left(-1 \cdot x\right) \cdot \left(a \cdot b - c \cdot i\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

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

Alternative 2: 37.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y2 \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-86}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) - \left(y4 \cdot t\_1 - y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{+141}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot t\_1 + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3))))
   (if (<= y2 -3.3e+118)
     (* y1 (* y2 (- (* k y4) (* x a))))
     (if (<= y2 -1.65e-86)
       (*
        y2
        (+
         (* k (- (* y1 y4) (* y0 y5)))
         (- (* t (- (* a y5) (* c y4))) (* x (- (* a y1) (* c y0))))))
       (if (<= y2 -5.2e-190)
         (*
          c
          (-
           (* i (- (* z t) (* x y)))
           (- (* y4 t_1) (* y0 (- (* x y2) (* z y3))))))
         (if (<= y2 2.2e-273)
           (*
            y1
            (* y4 (- (- (* k y2) (* j y3)) (/ (* i (- (* z k) (* x j))) y4))))
           (if (<= y2 1.02e+141)
             (*
              y4
              (-
               (* b (- (* t j) (* y k)))
               (+ (* c t_1) (* y1 (- (* j y3) (* k y2))))))
             (* y0 (* k (- (* z b) (* y2 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double tmp;
	if (y2 <= -3.3e+118) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -1.65e-86) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= -5.2e-190) {
		tmp = c * ((i * ((z * t) - (x * y))) - ((y4 * t_1) - (y0 * ((x * y2) - (z * y3)))));
	} else if (y2 <= 2.2e-273) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	} else if (y2 <= 1.02e+141) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * t_1) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    if (y2 <= (-3.3d+118)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y2 <= (-1.65d-86)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
    else if (y2 <= (-5.2d-190)) then
        tmp = c * ((i * ((z * t) - (x * y))) - ((y4 * t_1) - (y0 * ((x * y2) - (z * y3)))))
    else if (y2 <= 2.2d-273) then
        tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)))
    else if (y2 <= 1.02d+141) then
        tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * t_1) + (y1 * ((j * y3) - (k * y2)))))
    else
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double tmp;
	if (y2 <= -3.3e+118) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -1.65e-86) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= -5.2e-190) {
		tmp = c * ((i * ((z * t) - (x * y))) - ((y4 * t_1) - (y0 * ((x * y2) - (z * y3)))));
	} else if (y2 <= 2.2e-273) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	} else if (y2 <= 1.02e+141) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * t_1) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	tmp = 0
	if y2 <= -3.3e+118:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y2 <= -1.65e-86:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
	elif y2 <= -5.2e-190:
		tmp = c * ((i * ((z * t) - (x * y))) - ((y4 * t_1) - (y0 * ((x * y2) - (z * y3)))))
	elif y2 <= 2.2e-273:
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)))
	elif y2 <= 1.02e+141:
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * t_1) + (y1 * ((j * y3) - (k * y2)))))
	else:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y2 <= -3.3e+118)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -1.65e-86)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * Float64(Float64(a * y5) - Float64(c * y4))) - Float64(x * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y2 <= -5.2e-190)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) - Float64(Float64(y4 * t_1) - Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))));
	elseif (y2 <= 2.2e-273)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(Float64(k * y2) - Float64(j * y3)) - Float64(Float64(i * Float64(Float64(z * k) - Float64(x * j))) / y4))));
	elseif (y2 <= 1.02e+141)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) - Float64(Float64(c * t_1) + Float64(y1 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y2 <= -3.3e+118)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y2 <= -1.65e-86)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	elseif (y2 <= -5.2e-190)
		tmp = c * ((i * ((z * t) - (x * y))) - ((y4 * t_1) - (y0 * ((x * y2) - (z * y3)))));
	elseif (y2 <= 2.2e-273)
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	elseif (y2 <= 1.02e+141)
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * t_1) + (y1 * ((j * y3) - (k * y2)))));
	else
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.3e+118], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.65e-86], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.2e-190], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] - N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.2e-273], N[(y1 * N[(y4 * N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.02e+141], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -3.3e118

   1. Initial program 23.6%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 38.7%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 58.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -3.3e118 < y2 < -1.64999999999999993e-86

   1. Initial program 30.2%

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

   3. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(x \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(c \cdot y0 - a \cdot y1\right), x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(c \cdot y4\right), \color{blue}{\left(a \cdot y5\right)}\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y4\right), \left(\color{blue}{a} \cdot y5\right)\right)\right)\right)\right)\right) \]

   5. Simplified 51.7%

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

   if -1.64999999999999993e-86 < y2 < -5.1999999999999996e-190

   1. Initial program 30.1%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 52.7%

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

   if -5.1999999999999996e-190 < y2 < 2.1999999999999998e-273

   1. Initial program 39.3%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 50.9%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 54.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(y4 \cdot \left(-1 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)}, \mathsf{\_.f64}\left(0, y1\right)\right) \]
   10. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(-1 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       4. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y1\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       8. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       9. distribute-neg-out N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right) + \left(\mathsf{neg}\left(\left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

   11. Simplified 65.0%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(\frac{i \cdot \left(k \cdot z - j \cdot x\right)}{y4} - \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \cdot \left(0 - y1\right) \]

   if 2.1999999999999998e-273 < y2 < 1.02e141

   1. Initial program 35.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 59.8%

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

   if 1.02e141 < y2

   1. Initial program 11.6%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 26.1%

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

   6. Taylor expanded in k around -inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot k\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\left(y2 \cdot y5\right), \color{blue}{\left(b \cdot z\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \left(\color{blue}{b} \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 54.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-86}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) - \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{+141}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := z \cdot k - x \cdot j\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot t\_1\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-244}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot t\_2}{y4}\right)\right)\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot t\_1\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0))) (t_2 (- (* z k) (* x j))))
   (if (<= y -1.95e+64)
     (* c (* y (- (* y3 y4) (* x i))))
     (if (<= y -1.85e-69)
       (* z (- (* c (* t i)) (* k t_1)))
       (if (<= y 5.8e-244)
         (* y1 (* y4 (- (- (* k y2) (* j y3)) (/ (* i t_2) y4))))
         (if (<= y 6.3e+65)
           (*
            x
            (+
             (* y (- (* a b) (* c i)))
             (+ (* y2 (- (* c y0) (* a y1))) (* j t_1))))
           (if (<= y 2.6e+110)
             (*
              b
              (+
               (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
               (* y0 t_2)))
             (* k (* y (- (* i y5) (* b 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 t_1 = (i * y1) - (b * y0);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (y <= -1.95e+64) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y <= -1.85e-69) {
		tmp = z * ((c * (t * i)) - (k * t_1));
	} else if (y <= 5.8e-244) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_2) / y4)));
	} else if (y <= 6.3e+65) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * t_1)));
	} else if (y <= 2.6e+110) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	} else {
		tmp = k * (y * ((i * y5) - (b * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = (z * k) - (x * j)
    if (y <= (-1.95d+64)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y <= (-1.85d-69)) then
        tmp = z * ((c * (t * i)) - (k * t_1))
    else if (y <= 5.8d-244) then
        tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_2) / y4)))
    else if (y <= 6.3d+65) then
        tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * t_1)))
    else if (y <= 2.6d+110) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2))
    else
        tmp = k * (y * ((i * y5) - (b * 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 t_1 = (i * y1) - (b * y0);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (y <= -1.95e+64) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y <= -1.85e-69) {
		tmp = z * ((c * (t * i)) - (k * t_1));
	} else if (y <= 5.8e-244) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_2) / y4)));
	} else if (y <= 6.3e+65) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * t_1)));
	} else if (y <= 2.6e+110) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = (z * k) - (x * j)
	tmp = 0
	if y <= -1.95e+64:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y <= -1.85e-69:
		tmp = z * ((c * (t * i)) - (k * t_1))
	elif y <= 5.8e-244:
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_2) / y4)))
	elif y <= 6.3e+65:
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * t_1)))
	elif y <= 2.6e+110:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2))
	else:
		tmp = k * (y * ((i * y5) - (b * y4)))
	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(i * y1) - Float64(b * y0))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	tmp = 0.0
	if (y <= -1.95e+64)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y <= -1.85e-69)
		tmp = Float64(z * Float64(Float64(c * Float64(t * i)) - Float64(k * t_1)));
	elseif (y <= 5.8e-244)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(Float64(k * y2) - Float64(j * y3)) - Float64(Float64(i * t_2) / y4))));
	elseif (y <= 6.3e+65)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * t_1))));
	elseif (y <= 2.6e+110)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * t_2)));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * 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)
	t_1 = (i * y1) - (b * y0);
	t_2 = (z * k) - (x * j);
	tmp = 0.0;
	if (y <= -1.95e+64)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y <= -1.85e-69)
		tmp = z * ((c * (t * i)) - (k * t_1));
	elseif (y <= 5.8e-244)
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_2) / y4)));
	elseif (y <= 6.3e+65)
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * t_1)));
	elseif (y <= 2.6e+110)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	else
		tmp = k * (y * ((i * y5) - (b * y4)));
	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[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+64], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-69], N[(z * N[(N[(c * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(k * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-244], N[(y1 * N[(y4 * N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] - N[(N[(i * t$95$2), $MachinePrecision] / y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.3e+65], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+110], 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.9499999999999999e64

   1. Initial program 20.3%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 57.4%

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

   6. Taylor expanded in c around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(c \cdot \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(i \cdot x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y3, y4\right)\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -1.9499999999999999e64 < y < -1.8500000000000001e-69

   1. Initial program 31.9%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 45.4%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot t\right)\right)\right)}, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(\left(-1 \cdot c\right) \cdot \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 50.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \mathsf{*.f64}\left(i, t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

   8. Simplified 50.1%

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

   if -1.8500000000000001e-69 < y < 5.79999999999999992e-244

   1. Initial program 37.8%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 51.9%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 52.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(y4 \cdot \left(-1 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)}, \mathsf{\_.f64}\left(0, y1\right)\right) \]
   10. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(-1 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       4. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y1\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       8. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       9. distribute-neg-out N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right) + \left(\mathsf{neg}\left(\left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

   11. Simplified 55.1%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(\frac{i \cdot \left(k \cdot z - j \cdot x\right)}{y4} - \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \cdot \left(0 - y1\right) \]

   if 5.79999999999999992e-244 < y < 6.29999999999999997e65

   1. Initial program 31.8%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot \left(a \cdot b - c \cdot i\right)\right), \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(a \cdot b - c \cdot i\right) \cdot y\right), \left(\color{blue}{y2 \cdot \left(c \cdot y0 - a \cdot y1\right)} - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(a \cdot b - c \cdot i\right), y\right), \left(\color{blue}{y2 \cdot \left(c \cdot y0 - a \cdot y1\right)} - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right), y\right), \left(\color{blue}{y2} \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right), y\right), \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right), \left(\color{blue}{j} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(c \cdot y0 - a \cdot y1\right), y2\right), \left(\color{blue}{j} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right), y2\right), \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right), y2\right), \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), y2\right), \left(j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), y2\right), \mathsf{*.f64}\left(j, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right), y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), y2\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(b \cdot y0\right), \color{blue}{\left(i \cdot y1\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 49.0%

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

   if 6.29999999999999997e65 < y < 2.6e110

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 64.7%

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

   if 2.6e110 < y

   1. Initial program 21.2%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 55.1%

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

   6. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y} \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y} \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{i} \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 61.1%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-244}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -9.4 \cdot 10^{+117}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-113}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{+140}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -9.4e+117)
   (* y1 (* y2 (- (* k y4) (* x a))))
   (if (<= y2 -7.2e-113)
     (*
      y2
      (+
       (* k (- (* y1 y4) (* y0 y5)))
       (- (* t (- (* a y5) (* c y4))) (* x (- (* a y1) (* c y0))))))
     (if (<= y2 4.2e-257)
       (*
        i
        (+
         (* c (- (* z t) (* x y)))
         (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
       (if (<= y2 3.2e+140)
         (*
          y4
          (-
           (* b (- (* t j) (* y k)))
           (+ (* c (- (* t y2) (* y y3))) (* y1 (- (* j y3) (* k y2))))))
         (* y0 (* k (- (* z b) (* y2 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 (y2 <= -9.4e+117) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -7.2e-113) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= 4.2e-257) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y2 <= 3.2e+140) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= (-9.4d+117)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y2 <= (-7.2d-113)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
    else if (y2 <= 4.2d-257) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
    else if (y2 <= 3.2d+140) then
        tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))))
    else
        tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= -9.4e+117) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -7.2e-113) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= 4.2e-257) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	} else if (y2 <= 3.2e+140) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * 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 y2 <= -9.4e+117:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y2 <= -7.2e-113:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
	elif y2 <= 4.2e-257:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))))
	elif y2 <= 3.2e+140:
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))))
	else:
		tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= -9.4e+117)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -7.2e-113)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * Float64(Float64(a * y5) - Float64(c * y4))) - Float64(x * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y2 <= 4.2e-257)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y2 <= 3.2e+140)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) - Float64(Float64(c * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * 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 (y2 <= -9.4e+117)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y2 <= -7.2e-113)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	elseif (y2 <= 4.2e-257)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))));
	elseif (y2 <= 3.2e+140)
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	else
		tmp = y0 * (k * ((z * b) - (y2 * 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[y2, -9.4e+117], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7.2e-113], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e-257], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e+140], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -9.40000000000000011e117

   1. Initial program 23.6%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 38.7%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 58.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -9.40000000000000011e117 < y2 < -7.1999999999999995e-113

   1. Initial program 31.8%

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

   3. Taylor expanded in y2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(x \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(c \cdot y0 - a \cdot y1\right), x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(c \cdot y4\right), \color{blue}{\left(a \cdot y5\right)}\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y4\right), \left(\color{blue}{a} \cdot y5\right)\right)\right)\right)\right)\right) \]

   5. Simplified 49.1%

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

   if -7.1999999999999995e-113 < y2 < 4.2000000000000002e-257

   1. Initial program 35.9%

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

   3. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot i\right) \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot i\right), \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(\color{blue}{\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)} - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(c \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\left(c \cdot \left(x \cdot y - t \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y5 \cdot \left(j \cdot t - k \cdot y\right)} - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y5 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y5 \cdot \left(\color{blue}{j \cdot t} - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y5 \cdot \left(\color{blue}{j \cdot t} - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y5 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   if 4.2000000000000002e-257 < y2 < 3.20000000000000011e140

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 59.7%

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

   if 3.20000000000000011e140 < y2

   1. Initial program 11.6%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 26.1%

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

   6. Taylor expanded in k around -inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot k\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\left(y2 \cdot y5\right), \color{blue}{\left(b \cdot z\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \left(\color{blue}{b} \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 54.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9.4 \cdot 10^{+117}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -7.2 \cdot 10^{-113}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{+140}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -7.5e+118)
   (* y1 (* y2 (- (* k y4) (* x a))))
   (if (<= y2 -2.7e+47)
     (*
      y2
      (+
       (* k (- (* y1 y4) (* y0 y5)))
       (- (* t (- (* a y5) (* c y4))) (* x (- (* a y1) (* c y0))))))
     (if (<= y2 -2.5e-207)
       (* z (- (* c (* t i)) (* k (- (* i y1) (* b y0)))))
       (if (<= y2 9.5e+139)
         (*
          y4
          (-
           (* b (- (* t j) (* y k)))
           (+ (* c (- (* t y2) (* y y3))) (* y1 (- (* j y3) (* k y2))))))
         (* y0 (* k (- (* z b) (* y2 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 (y2 <= -7.5e+118) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -2.7e+47) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= -2.5e-207) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 9.5e+139) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= (-7.5d+118)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y2 <= (-2.7d+47)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
    else if (y2 <= (-2.5d-207)) then
        tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
    else if (y2 <= 9.5d+139) then
        tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))))
    else
        tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= -7.5e+118) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y2 <= -2.7e+47) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	} else if (y2 <= -2.5e-207) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 9.5e+139) {
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * 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 y2 <= -7.5e+118:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y2 <= -2.7e+47:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))))
	elif y2 <= -2.5e-207:
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
	elif y2 <= 9.5e+139:
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))))
	else:
		tmp = y0 * (k * ((z * b) - (y2 * 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 (y2 <= -7.5e+118)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y2 <= -2.7e+47)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(t * Float64(Float64(a * y5) - Float64(c * y4))) - Float64(x * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y2 <= -2.5e-207)
		tmp = Float64(z * Float64(Float64(c * Float64(t * i)) - Float64(k * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 9.5e+139)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) - Float64(Float64(c * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * 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 (y2 <= -7.5e+118)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y2 <= -2.7e+47)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((t * ((a * y5) - (c * y4))) - (x * ((a * y1) - (c * y0)))));
	elseif (y2 <= -2.5e-207)
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	elseif (y2 <= 9.5e+139)
		tmp = y4 * ((b * ((t * j) - (y * k))) - ((c * ((t * y2) - (y * y3))) + (y1 * ((j * y3) - (k * y2)))));
	else
		tmp = y0 * (k * ((z * b) - (y2 * 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[y2, -7.5e+118], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.7e+47], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.5e-207], N[(z * N[(N[(c * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+139], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -7.50000000000000003e118

   1. Initial program 23.6%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 38.7%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 58.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 58.0%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -7.50000000000000003e118 < y2 < -2.69999999999999996e47

   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 y2 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \color{blue}{\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{x \cdot \left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(x \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(x \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(c \cdot y0 - a \cdot y1\right), x\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(c \cdot y4\right), \color{blue}{\left(a \cdot y5\right)}\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{+.f64}\left(\mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right), x\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y4\right), \left(\color{blue}{a} \cdot y5\right)\right)\right)\right)\right)\right) \]

   5. Simplified 70.0%

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

   if -2.69999999999999996e47 < y2 < -2.50000000000000007e-207

   1. Initial program 31.4%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 36.4%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot t\right)\right)\right)}, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(\left(-1 \cdot c\right) \cdot \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \mathsf{*.f64}\left(i, t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

   8. Simplified 43.3%

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

   if -2.50000000000000007e-207 < y2 < 9.5000000000000002e139

   1. Initial program 37.1%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 57.9%

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

   if 9.5000000000000002e139 < y2

   1. Initial program 11.6%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 26.1%

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

   6. Taylor expanded in k around -inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot k\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\left(y2 \cdot y5\right), \color{blue}{\left(b \cdot z\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \left(\color{blue}{b} \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 54.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - x \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+139}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) - \left(c \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot k - x \cdot j\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot t\_1\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+106}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot t\_1}{y4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z k) (* x j)))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 t_1)))))
   (if (<= b -2.3e+164)
     t_2
     (if (<= b 1.26e+106)
       (* y1 (* y4 (- (- (* k y2) (* j y3)) (/ (* i t_1) y4))))
       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 = (z * k) - (x * j);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_1));
	double tmp;
	if (b <= -2.3e+164) {
		tmp = t_2;
	} else if (b <= 1.26e+106) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_1) / y4)));
	} 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 = (z * k) - (x * j)
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_1))
    if (b <= (-2.3d+164)) then
        tmp = t_2
    else if (b <= 1.26d+106) then
        tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_1) / y4)))
    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 = (z * k) - (x * j);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_1));
	double tmp;
	if (b <= -2.3e+164) {
		tmp = t_2;
	} else if (b <= 1.26e+106) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_1) / y4)));
	} 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 = (z * k) - (x * j)
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_1))
	tmp = 0
	if b <= -2.3e+164:
		tmp = t_2
	elif b <= 1.26e+106:
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_1) / y4)))
	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(Float64(z * k) - Float64(x * j))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * t_1)))
	tmp = 0.0
	if (b <= -2.3e+164)
		tmp = t_2;
	elseif (b <= 1.26e+106)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(Float64(k * y2) - Float64(j * y3)) - Float64(Float64(i * t_1) / y4))));
	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 = (z * k) - (x * j);
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_1));
	tmp = 0.0;
	if (b <= -2.3e+164)
		tmp = t_2;
	elseif (b <= 1.26e+106)
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * t_1) / y4)));
	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[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+164], t$95$2, If[LessEqual[b, 1.26e+106], N[(y1 * N[(y4 * N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] - N[(N[(i * t$95$1), $MachinePrecision] / y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3e164 or 1.25999999999999991e106 < 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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 59.1%

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

   if -2.3e164 < b < 1.25999999999999991e106

   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 y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 44.3%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 42.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(y4 \cdot \left(-1 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)}, \mathsf{\_.f64}\left(0, y1\right)\right) \]
   10. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(-1 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       4. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y1\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       8. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       9. distribute-neg-out N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right) + \left(\mathsf{neg}\left(\left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

   11. Simplified 46.4%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(\frac{i \cdot \left(k \cdot z - j \cdot x\right)}{y4} - \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \cdot \left(0 - y1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+106}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-121}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -3.5e+140)
   (* b (* a (- (* x y) (* z t))))
   (if (<= z -7.8e-76)
     (* y0 (* c (- (* x y2) (* z y3))))
     (if (<= z 4.4e-121)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= z 3.9e-54)
         (* y (* y5 (- (* i k) (* a y3))))
         (if (<= z 4.2e+131)
           (* y4 (* c (- (* y y3) (* t y2))))
           (* y1 (* i (- (* x j) (* z 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 tmp;
	if (z <= -3.5e+140) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= -7.8e-76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (z <= 4.4e-121) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (z <= 3.9e-54) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (z <= 4.2e+131) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (i * ((x * j) - (z * 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) :: tmp
    if (z <= (-3.5d+140)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (z <= (-7.8d-76)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (z <= 4.4d-121) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (z <= 3.9d-54) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (z <= 4.2d+131) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else
        tmp = y1 * (i * ((x * j) - (z * 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 tmp;
	if (z <= -3.5e+140) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= -7.8e-76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (z <= 4.4e-121) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (z <= 3.9e-54) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (z <= 4.2e+131) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = y1 * (i * ((x * j) - (z * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -3.5e+140:
		tmp = b * (a * ((x * y) - (z * t)))
	elif z <= -7.8e-76:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif z <= 4.4e-121:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif z <= 3.9e-54:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif z <= 4.2e+131:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	else:
		tmp = y1 * (i * ((x * j) - (z * k)))
	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 (z <= -3.5e+140)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (z <= -7.8e-76)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (z <= 4.4e-121)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (z <= 3.9e-54)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (z <= 4.2e+131)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * 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)
	tmp = 0.0;
	if (z <= -3.5e+140)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (z <= -7.8e-76)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (z <= 4.4e-121)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (z <= 3.9e-54)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (z <= 4.2e+131)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	else
		tmp = y1 * (i * ((x * j) - (z * k)));
	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[z, -3.5e+140], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-76], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-121], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-54], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+131], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.49999999999999989e140

   1. Initial program 25.5%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 41.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 44.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 44.7%

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

   if -3.49999999999999989e140 < z < -7.8000000000000005e-76

   1. Initial program 27.4%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 36.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.5%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 38.5%

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

   if -7.8000000000000005e-76 < z < 4.40000000000000042e-121

   1. Initial program 34.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 38.2%

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

   6. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.1%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 38.1%

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

   if 4.40000000000000042e-121 < z < 3.9e-54

   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

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 46.7%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 69.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 69.6%

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

   if 3.9e-54 < z < 4.19999999999999971e131

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 53.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 62.4%

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

   if 4.19999999999999971e131 < z

   1. Initial program 19.4%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 51.6%

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

   6. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(i \cdot y1\right), \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, y1\right), \left(\color{blue}{j \cdot x} - k \cdot z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \left(\color{blue}{k} \cdot z\right)\right)\right) \]

      6. *-lowering-*.f64 52.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 52.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{y1}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot x - k \cdot z\right)\right), y1\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot x\right), \left(k \cdot z\right)\right)\right), y1\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \left(k \cdot z\right)\right)\right), y1\right) \]

      8. *-lowering-*.f64 68.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right), y1\right) \]

   10. Applied egg-rr 68.3%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-121}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+131}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+139}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+150}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.2e+139)
   (* b (* a (- (* x y) (* z t))))
   (if (<= z -9.2e-76)
     (* y0 (* c (- (* x y2) (* z y3))))
     (if (<= z 3.6e-121)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (if (<= z 3e-58)
         (* y (* y5 (- (* i k) (* a y3))))
         (if (<= z 5.9e+150)
           (* y4 (* c (- (* y y3) (* t y2))))
           (* (* z i) (- (* t c) (* k 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 tmp;
	if (z <= -2.2e+139) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= -9.2e-76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (z <= 3.6e-121) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (z <= 3e-58) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (z <= 5.9e+150) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = (z * i) * ((t * c) - (k * 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) :: tmp
    if (z <= (-2.2d+139)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (z <= (-9.2d-76)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (z <= 3.6d-121) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (z <= 3d-58) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (z <= 5.9d+150) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else
        tmp = (z * i) * ((t * c) - (k * 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 tmp;
	if (z <= -2.2e+139) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (z <= -9.2e-76) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (z <= 3.6e-121) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (z <= 3e-58) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (z <= 5.9e+150) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = (z * i) * ((t * c) - (k * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -2.2e+139:
		tmp = b * (a * ((x * y) - (z * t)))
	elif z <= -9.2e-76:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif z <= 3.6e-121:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif z <= 3e-58:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif z <= 5.9e+150:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	else:
		tmp = (z * i) * ((t * c) - (k * y1))
	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 (z <= -2.2e+139)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (z <= -9.2e-76)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (z <= 3.6e-121)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (z <= 3e-58)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (z <= 5.9e+150)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(Float64(z * i) * Float64(Float64(t * c) - Float64(k * 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)
	tmp = 0.0;
	if (z <= -2.2e+139)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (z <= -9.2e-76)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (z <= 3.6e-121)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (z <= 3e-58)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (z <= 5.9e+150)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	else
		tmp = (z * i) * ((t * c) - (k * y1));
	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[z, -2.2e+139], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e-76], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-121], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-58], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+150], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.1999999999999999e139

   1. Initial program 25.5%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 41.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 44.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 44.7%

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

   if -2.1999999999999999e139 < z < -9.20000000000000025e-76

   1. Initial program 27.4%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 36.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.5%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 38.5%

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

   if -9.20000000000000025e-76 < z < 3.59999999999999984e-121

   1. Initial program 34.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 38.2%

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

   6. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.1%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 38.1%

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

   if 3.59999999999999984e-121 < z < 3.00000000000000008e-58

   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

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 46.7%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 69.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 69.6%

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

   if 3.00000000000000008e-58 < z < 5.90000000000000023e150

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 56.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 62.1%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 62.1%

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

   if 5.90000000000000023e150 < z

   1. Initial program 19.2%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 65.4%

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

   6. Taylor expanded in i around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(i \cdot z\right), \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{c \cdot t} - k \cdot y1\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right) \]

      6. *-lowering-*.f64 59.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right) \]

   8. Simplified 59.4%

      \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(c \cdot t - k \cdot y1\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+139}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-76}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+150}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \left(t \cdot c - k \cdot y1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-206}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -8.2e+111)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -8.2e-76)
     (* y4 (* c (- (* y y3) (* t y2))))
     (if (<= a -7.6e-206)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= a 1.55e-118)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= a 4.9e+100)
           (* y4 (* y1 (- (* k y2) (* j y3))))
           (* y (* y5 (- (* i k) (* a y3))))))))))

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 (a <= -8.2e+111) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -8.2e-76) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (a <= -7.6e-206) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 1.55e-118) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 4.9e+100) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	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 (a <= (-8.2d+111)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-8.2d-76)) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (a <= (-7.6d-206)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (a <= 1.55d-118) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= 4.9d+100) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    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 (a <= -8.2e+111) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -8.2e-76) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (a <= -7.6e-206) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 1.55e-118) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 4.9e+100) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -8.2e+111:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -8.2e-76:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif a <= -7.6e-206:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif a <= 1.55e-118:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= 4.9e+100:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	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 (a <= -8.2e+111)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -8.2e-76)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= -7.6e-206)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (a <= 1.55e-118)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= 4.9e+100)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	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 (a <= -8.2e+111)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -8.2e-76)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (a <= -7.6e-206)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (a <= 1.55e-118)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= 4.9e+100)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	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[a, -8.2e+111], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-76], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.6e-206], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-118], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+100], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.19999999999999973e111

   1. Initial program 20.6%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 50.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 60.1%

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

   if -8.19999999999999973e111 < a < -8.1999999999999996e-76

   1. Initial program 37.8%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 44.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 46.9%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 46.9%

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

   if -8.1999999999999996e-76 < a < -7.60000000000000005e-206

   1. Initial program 34.2%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 31.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(b \cdot j\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{b} \cdot j\right)\right)\right)\right) \]

      4. *-lowering-*.f64 41.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(b, \color{blue}{j}\right)\right)\right)\right) \]

   8. Simplified 41.1%

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

   if -7.60000000000000005e-206 < a < 1.5500000000000001e-118

   1. Initial program 26.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 38.1%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 42.2%

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

   if 1.5500000000000001e-118 < a < 4.89999999999999967e100

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 31.3%

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

   6. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.8%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 39.8%

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

   if 4.89999999999999967e100 < a

   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 y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 41.8%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-206}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-77}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-209}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 265000000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+86}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -2.7e+109)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -7.5e-77)
     (* y4 (* c (- (* y y3) (* t y2))))
     (if (<= a -4.8e-209)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= a 265000000000.0)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= a 2.35e+86)
           (* (* a y3) (* z y1))
           (* y (* y5 (- (* i k) (* a y3))))))))))

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 (a <= -2.7e+109) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7.5e-77) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (a <= -4.8e-209) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 265000000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 2.35e+86) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	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 (a <= (-2.7d+109)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-7.5d-77)) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (a <= (-4.8d-209)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (a <= 265000000000.0d0) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= 2.35d+86) then
        tmp = (a * y3) * (z * y1)
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    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 (a <= -2.7e+109) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7.5e-77) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (a <= -4.8e-209) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 265000000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 2.35e+86) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -2.7e+109:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -7.5e-77:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif a <= -4.8e-209:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif a <= 265000000000.0:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= 2.35e+86:
		tmp = (a * y3) * (z * y1)
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	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 (a <= -2.7e+109)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -7.5e-77)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= -4.8e-209)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (a <= 265000000000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= 2.35e+86)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	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 (a <= -2.7e+109)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -7.5e-77)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (a <= -4.8e-209)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (a <= 265000000000.0)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= 2.35e+86)
		tmp = (a * y3) * (z * y1);
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	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[a, -2.7e+109], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-77], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-209], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 265000000000.0], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+86], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.70000000000000001e109

   1. Initial program 20.6%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 50.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 60.1%

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

   if -2.70000000000000001e109 < a < -7.5000000000000006e-77

   1. Initial program 37.8%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 44.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 46.9%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 46.9%

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

   if -7.5000000000000006e-77 < a < -4.8000000000000002e-209

   1. Initial program 34.2%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 31.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(b \cdot j\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{b} \cdot j\right)\right)\right)\right) \]

      4. *-lowering-*.f64 41.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(b, \color{blue}{j}\right)\right)\right)\right) \]

   8. Simplified 41.1%

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

   if -4.8000000000000002e-209 < a < 2.65e11

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 34.4%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 36.3%

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

   if 2.65e11 < a < 2.3500000000000001e86

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.8%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 43.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 43.4%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 43.6%

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

   if 2.3500000000000001e86 < a

   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 y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 42.2%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-77}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-209}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 265000000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+86}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-212}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 245000000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -8.4e+40)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -2.15e-73)
     (* c (* y (* y3 y4)))
     (if (<= a -1.25e-212)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= a 245000000000.0)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= a 1.5e+77)
           (* (* a y3) (* z y1))
           (* y (* y5 (- (* i k) (* a y3))))))))))

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 (a <= -8.4e+40) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -2.15e-73) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= -1.25e-212) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 245000000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 1.5e+77) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	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 (a <= (-8.4d+40)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-2.15d-73)) then
        tmp = c * (y * (y3 * y4))
    else if (a <= (-1.25d-212)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (a <= 245000000000.0d0) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= 1.5d+77) then
        tmp = (a * y3) * (z * y1)
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    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 (a <= -8.4e+40) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -2.15e-73) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= -1.25e-212) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (a <= 245000000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 1.5e+77) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -8.4e+40:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -2.15e-73:
		tmp = c * (y * (y3 * y4))
	elif a <= -1.25e-212:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif a <= 245000000000.0:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= 1.5e+77:
		tmp = (a * y3) * (z * y1)
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	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 (a <= -8.4e+40)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -2.15e-73)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (a <= -1.25e-212)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (a <= 245000000000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= 1.5e+77)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	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 (a <= -8.4e+40)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -2.15e-73)
		tmp = c * (y * (y3 * y4));
	elseif (a <= -1.25e-212)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (a <= 245000000000.0)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= 1.5e+77)
		tmp = (a * y3) * (z * y1);
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	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[a, -8.4e+40], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.15e-73], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-212], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 245000000000.0], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+77], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -8.4000000000000004e40

   1. Initial program 23.8%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -8.4000000000000004e40 < a < -2.1499999999999999e-73

   1. Initial program 37.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 38.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 49.3%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 49.3%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 49.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 49.4%

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

   if -2.1499999999999999e-73 < a < -1.25000000000000011e-212

   1. Initial program 34.2%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 31.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(b \cdot j\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{b} \cdot j\right)\right)\right)\right) \]

      4. *-lowering-*.f64 41.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(b, \color{blue}{j}\right)\right)\right)\right) \]

   8. Simplified 41.1%

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

   if -1.25000000000000011e-212 < a < 2.45e11

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 34.4%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 36.3%

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

   if 2.45e11 < a < 1.4999999999999999e77

   1. Initial program 29.3%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 47.9%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 42.6%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 42.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 42.9%

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

   if 1.4999999999999999e77 < a

   1. Initial program 21.2%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 40.5%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-212}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 245000000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= y3 -1.68e+218)
     (* (* a y3) (* z y1))
     (if (<= y3 -5.5e+48)
       (* c (* y (* y3 y4)))
       (if (<= y3 1.55e-214)
         t_1
         (if (<= y3 4.2e-31)
           (- 0.0 (* y0 (* y5 (* k y2))))
           (if (<= y3 2.9e+127) t_1 (* y4 (* c (* y y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -1.68e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -5.5e+48) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 1.55e-214) {
		tmp = t_1;
	} else if (y3 <= 4.2e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 2.9e+127) {
		tmp = t_1;
	} else {
		tmp = y4 * (c * (y * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (y3 <= (-1.68d+218)) then
        tmp = (a * y3) * (z * y1)
    else if (y3 <= (-5.5d+48)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 1.55d-214) then
        tmp = t_1
    else if (y3 <= 4.2d-31) then
        tmp = 0.0d0 - (y0 * (y5 * (k * y2)))
    else if (y3 <= 2.9d+127) then
        tmp = t_1
    else
        tmp = y4 * (c * (y * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (y3 <= -1.68e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -5.5e+48) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 1.55e-214) {
		tmp = t_1;
	} else if (y3 <= 4.2e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 2.9e+127) {
		tmp = t_1;
	} else {
		tmp = y4 * (c * (y * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if y3 <= -1.68e+218:
		tmp = (a * y3) * (z * y1)
	elif y3 <= -5.5e+48:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 1.55e-214:
		tmp = t_1
	elif y3 <= 4.2e-31:
		tmp = 0.0 - (y0 * (y5 * (k * y2)))
	elif y3 <= 2.9e+127:
		tmp = t_1
	else:
		tmp = y4 * (c * (y * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y3 <= -1.68e+218)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	elseif (y3 <= -5.5e+48)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 1.55e-214)
		tmp = t_1;
	elseif (y3 <= 4.2e-31)
		tmp = Float64(0.0 - Float64(y0 * Float64(y5 * Float64(k * y2))));
	elseif (y3 <= 2.9e+127)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y3 <= -1.68e+218)
		tmp = (a * y3) * (z * y1);
	elseif (y3 <= -5.5e+48)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 1.55e-214)
		tmp = t_1;
	elseif (y3 <= 4.2e-31)
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	elseif (y3 <= 2.9e+127)
		tmp = t_1;
	else
		tmp = y4 * (c * (y * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.68e+218], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.5e+48], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.55e-214], t$95$1, If[LessEqual[y3, 4.2e-31], N[(0.0 - N[(y0 * N[(y5 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.9e+127], t$95$1, N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.6800000000000001e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 58.2%

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

   if -1.6800000000000001e218 < y3 < -5.5000000000000002e48

   1. Initial program 8.8%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.7%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 42.7%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 51.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 51.3%

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

   if -5.5000000000000002e48 < y3 < 1.55000000000000002e-214 or 4.19999999999999982e-31 < y3 < 2.9000000000000002e127

   1. Initial program 34.9%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 42.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 34.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 34.3%

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

   if 1.55000000000000002e-214 < y3 < 4.19999999999999982e-31

   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 y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 33.1%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 43.3%

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

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \color{blue}{\left(k \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 40.9%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{*.f64}\left(k, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 40.9%

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

   if 2.9000000000000002e127 < y3

   1. Initial program 28.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 54.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+40}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 6.4 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= y2 -2.15e+63)
     t_1
     (if (<= y2 -2.2e-208)
       (* z (- (* c (* t i)) (* k (- (* i y1) (* b y0)))))
       (if (<= y2 6.6e+40)
         (* y1 (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3)))))
         (if (<= y2 6.4e+209) (* 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -2.15e+63) {
		tmp = t_1;
	} else if (y2 <= -2.2e-208) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 6.6e+40) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (y2 <= 6.4e+209) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
    if (y2 <= (-2.15d+63)) then
        tmp = t_1
    else if (y2 <= (-2.2d-208)) then
        tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
    else if (y2 <= 6.6d+40) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
    else if (y2 <= 6.4d+209) then
        tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -2.15e+63) {
		tmp = t_1;
	} else if (y2 <= -2.2e-208) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 6.6e+40) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (y2 <= 6.4e+209) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if y2 <= -2.15e+63:
		tmp = t_1
	elif y2 <= -2.2e-208:
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
	elif y2 <= 6.6e+40:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
	elif y2 <= 6.4e+209:
		tmp = 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(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (y2 <= -2.15e+63)
		tmp = t_1;
	elseif (y2 <= -2.2e-208)
		tmp = Float64(z * Float64(Float64(c * Float64(t * i)) - Float64(k * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 6.6e+40)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))));
	elseif (y2 <= 6.4e+209)
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (y2 <= -2.15e+63)
		tmp = t_1;
	elseif (y2 <= -2.2e-208)
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	elseif (y2 <= 6.6e+40)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	elseif (y2 <= 6.4e+209)
		tmp = 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[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.15e+63], t$95$1, If[LessEqual[y2, -2.2e-208], N[(z * N[(N[(c * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.6e+40], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.4e+209], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -2.15e63 or 6.3999999999999999e209 < y2

   1. Initial program 17.7%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 54.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 54.6%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -2.15e63 < y2 < -2.2e-208

   1. Initial program 32.1%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 38.2%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot t\right)\right)\right)}, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(\left(-1 \cdot c\right) \cdot \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 43.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \mathsf{*.f64}\left(i, t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

   8. Simplified 43.1%

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

   if -2.2e-208 < y2 < 6.5999999999999997e40

   1. Initial program 36.6%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 47.4%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   if 6.5999999999999997e40 < y2 < 6.3999999999999999e209

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 52.1%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 64.6%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+63}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+40}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 6.4 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-243}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - y4 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-81}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot \left(y2 - \frac{y \cdot b}{y1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -9.2e+70)
   (* c (* y (- (* y3 y4) (* x i))))
   (if (<= y 9.2e-243)
     (* y1 (- (* i (- (* x j) (* z k))) (* y4 (* j y3))))
     (if (<= y 7.8e-81)
       (* y0 (* k (- (* z b) (* y2 y5))))
       (if (<= y 7.8e+139)
         (* y4 (* k (* y1 (- y2 (/ (* y b) y1)))))
         (* k (* y (- (* i y5) (* b 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 (y <= -9.2e+70) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y <= 9.2e-243) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	} else if (y <= 7.8e-81) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (y <= 7.8e+139) {
		tmp = y4 * (k * (y1 * (y2 - ((y * b) / y1))));
	} else {
		tmp = k * (y * ((i * y5) - (b * 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 (y <= (-9.2d+70)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y <= 9.2d-243) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)))
    else if (y <= 7.8d-81) then
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    else if (y <= 7.8d+139) then
        tmp = y4 * (k * (y1 * (y2 - ((y * b) / y1))))
    else
        tmp = k * (y * ((i * y5) - (b * 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 (y <= -9.2e+70) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y <= 9.2e-243) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	} else if (y <= 7.8e-81) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (y <= 7.8e+139) {
		tmp = y4 * (k * (y1 * (y2 - ((y * b) / y1))));
	} else {
		tmp = k * (y * ((i * y5) - (b * 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 y <= -9.2e+70:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y <= 9.2e-243:
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)))
	elif y <= 7.8e-81:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	elif y <= 7.8e+139:
		tmp = y4 * (k * (y1 * (y2 - ((y * b) / y1))))
	else:
		tmp = k * (y * ((i * y5) - (b * 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 (y <= -9.2e+70)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y <= 9.2e-243)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(y4 * Float64(j * y3))));
	elseif (y <= 7.8e-81)
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y <= 7.8e+139)
		tmp = Float64(y4 * Float64(k * Float64(y1 * Float64(y2 - Float64(Float64(y * b) / y1)))));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * 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 (y <= -9.2e+70)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y <= 9.2e-243)
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	elseif (y <= 7.8e-81)
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	elseif (y <= 7.8e+139)
		tmp = y4 * (k * (y1 * (y2 - ((y * b) / y1))));
	else
		tmp = k * (y * ((i * y5) - (b * 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[y, -9.2e+70], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-243], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-81], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+139], N[(y4 * N[(k * N[(y1 * N[(y2 - N[(N[(y * b), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.19999999999999975e70

   1. Initial program 20.3%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 57.4%

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

   6. Taylor expanded in c around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(c \cdot \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(i \cdot x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y3, y4\right)\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -9.19999999999999975e70 < y < 9.20000000000000001e-243

   1. Initial program 36.2%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 46.5%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y2 around 0

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

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \color{blue}{\left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \left(j \cdot \left(y3 \cdot y4\right) + \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(j \cdot \left(y3 \cdot y4\right)\right), \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(j \cdot \left(y4 \cdot y3\right)\right), \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(\left(j \cdot y4\right) \cdot y3\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(\left(y4 \cdot j\right) \cdot y3\right), \left(\mathsf{neg}\left(\color{blue}{i} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(y4 \cdot \left(j \cdot y3\right)\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \left(j \cdot y3\right)\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       13. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right) \]

       14. neg-mul-1 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right)\right)\right)\right) \]

       15. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(j \cdot x + \color{blue}{\left(\mathsf{neg}\left(k \cdot z\right)\right)}\right)\right)\right)\right)\right) \]

       16. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\left(\mathsf{neg}\left(k \cdot z\right)\right) + \color{blue}{j \cdot x}\right)\right)\right)\right)\right) \]

       17. distribute-lft-in N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\mathsf{neg}\left(k \cdot z\right)\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot x\right)}\right)\right)\right)\right) \]

   11. Simplified 45.9%

       \[\leadsto \color{blue}{0 - y1 \cdot \left(y4 \cdot \left(j \cdot y3\right) + i \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 9.20000000000000001e-243 < y < 7.7999999999999997e-81

   1. Initial program 29.0%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 39.7%

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

   6. Taylor expanded in k around -inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot k\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y2 \cdot y5} - b \cdot z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\left(y2 \cdot y5\right), \color{blue}{\left(b \cdot z\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \left(\color{blue}{b} \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 47.1%

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

   if 7.7999999999999997e-81 < y < 7.80000000000000012e139

   1. Initial program 35.3%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 39.8%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 32.8%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 32.8%

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

   9. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 + -1 \cdot \frac{b \cdot y}{y1}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 + -1 \cdot \frac{b \cdot y}{y1}\right)}\right)\right)\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y2 + \left(\mathsf{neg}\left(\frac{b \cdot y}{y1}\right)\right)\right)\right)\right)\right) \]

       3. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y2 - \color{blue}{\frac{b \cdot y}{y1}}\right)\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(y2, \color{blue}{\left(\frac{b \cdot y}{y1}\right)}\right)\right)\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(y2, \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{y1}\right)\right)\right)\right)\right) \]

       6. *-lowering-*.f64 40.2%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(y2, \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, y\right), y1\right)\right)\right)\right)\right) \]

   11. Simplified 40.2%

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

   if 7.80000000000000012e139 < y

   1. Initial program 21.4%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 60.9%

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

   6. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot k\right), \color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(k\right)\right), \left(\color{blue}{y} \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \left(\color{blue}{y} \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{i} \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(k\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 61.2%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-243}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - y4 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-81}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot \left(y2 - \frac{y \cdot b}{y1}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;y2 \leq -5.4 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= y2 -5.4e+127)
     t_1
     (if (<= y2 2.3e+42)
       (* y1 (* y4 (- (- (* k y2) (* j y3)) (/ (* i (- (* z k) (* x j))) y4))))
       (if (<= y2 6.2e+209) (* 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -5.4e+127) {
		tmp = t_1;
	} else if (y2 <= 2.3e+42) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	} else if (y2 <= 6.2e+209) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
    if (y2 <= (-5.4d+127)) then
        tmp = t_1
    else if (y2 <= 2.3d+42) then
        tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)))
    else if (y2 <= 6.2d+209) then
        tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -5.4e+127) {
		tmp = t_1;
	} else if (y2 <= 2.3e+42) {
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	} else if (y2 <= 6.2e+209) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if y2 <= -5.4e+127:
		tmp = t_1
	elif y2 <= 2.3e+42:
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)))
	elif y2 <= 6.2e+209:
		tmp = 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(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (y2 <= -5.4e+127)
		tmp = t_1;
	elseif (y2 <= 2.3e+42)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(Float64(k * y2) - Float64(j * y3)) - Float64(Float64(i * Float64(Float64(z * k) - Float64(x * j))) / y4))));
	elseif (y2 <= 6.2e+209)
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (y2 <= -5.4e+127)
		tmp = t_1;
	elseif (y2 <= 2.3e+42)
		tmp = y1 * (y4 * (((k * y2) - (j * y3)) - ((i * ((z * k) - (x * j))) / y4)));
	elseif (y2 <= 6.2e+209)
		tmp = 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[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.4e+127], t$95$1, If[LessEqual[y2, 2.3e+42], N[(y1 * N[(y4 * N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.2e+209], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -5.4000000000000004e127 or 6.2000000000000002e209 < y2

   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 y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 35.8%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 60.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 60.4%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -5.4000000000000004e127 < y2 < 2.3e42

   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 y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 43.8%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 42.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(y4 \cdot \left(-1 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)}, \mathsf{\_.f64}\left(0, y1\right)\right) \]
   10. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(-1 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 - j \cdot y3\right) + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       4. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y4 \cdot \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(k \cdot y2 + \frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y1\right)\right) \]

       7. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + k \cdot y2\right) - j \cdot y3\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       8. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\mathsf{neg}\left(\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4} + \left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

       9. distribute-neg-out N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, \left(\left(\mathsf{neg}\left(\frac{i \cdot \left(j \cdot x - k \cdot z\right)}{y4}\right)\right) + \left(\mathsf{neg}\left(\left(k \cdot y2 - j \cdot y3\right)\right)\right)\right)\right), \mathsf{\_.f64}\left(0, y1\right)\right) \]

   11. Simplified 45.9%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(\frac{i \cdot \left(k \cdot z - j \cdot x\right)}{y4} - \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \cdot \left(0 - y1\right) \]

   if 2.3e42 < y2 < 6.2000000000000002e209

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 52.1%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 64.6%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.4 \cdot 10^{+127}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{+42}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(\left(k \cdot y2 - j \cdot y3\right) - \frac{i \cdot \left(z \cdot k - x \cdot j\right)}{y4}\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.56 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(\left(z \cdot t\right) \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y3 \leq 3.7 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.56e+218)
   (* (* a y3) (* z y1))
   (if (<= y3 -7.5e-24)
     (* c (* y (* y3 y4)))
     (if (<= y3 1.2e-214)
       (* b (* (* z t) (- 0.0 a)))
       (if (<= y3 3.7e-31)
         (- 0.0 (* y0 (* y5 (* k y2))))
         (if (<= y3 2.1e+127) (* y (* b (* x a))) (* y4 (* c (* y y3)))))))))

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 <= -1.56e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -7.5e-24) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 1.2e-214) {
		tmp = b * ((z * t) * (0.0 - a));
	} else if (y3 <= 3.7e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.56d+218)) then
        tmp = (a * y3) * (z * y1)
    else if (y3 <= (-7.5d-24)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 1.2d-214) then
        tmp = b * ((z * t) * (0.0d0 - a))
    else if (y3 <= 3.7d-31) then
        tmp = 0.0d0 - (y0 * (y5 * (k * y2)))
    else if (y3 <= 2.1d+127) then
        tmp = y * (b * (x * a))
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.56e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -7.5e-24) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 1.2e-214) {
		tmp = b * ((z * t) * (0.0 - a));
	} else if (y3 <= 3.7e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.56e+218:
		tmp = (a * y3) * (z * y1)
	elif y3 <= -7.5e-24:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 1.2e-214:
		tmp = b * ((z * t) * (0.0 - a))
	elif y3 <= 3.7e-31:
		tmp = 0.0 - (y0 * (y5 * (k * y2)))
	elif y3 <= 2.1e+127:
		tmp = y * (b * (x * a))
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.56e+218)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	elseif (y3 <= -7.5e-24)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 1.2e-214)
		tmp = Float64(b * Float64(Float64(z * t) * Float64(0.0 - a)));
	elseif (y3 <= 3.7e-31)
		tmp = Float64(0.0 - Float64(y0 * Float64(y5 * Float64(k * y2))));
	elseif (y3 <= 2.1e+127)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.56e+218)
		tmp = (a * y3) * (z * y1);
	elseif (y3 <= -7.5e-24)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 1.2e-214)
		tmp = b * ((z * t) * (0.0 - a));
	elseif (y3 <= 3.7e-31)
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	elseif (y3 <= 2.1e+127)
		tmp = y * (b * (x * a));
	else
		tmp = y4 * (c * (y * y3));
	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, -1.56e+218], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7.5e-24], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.2e-214], N[(b * N[(N[(z * t), $MachinePrecision] * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.7e-31], N[(0.0 - N[(y0 * N[(y5 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e+127], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -1.55999999999999997e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 58.2%

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

   if -1.55999999999999997e218 < y3 < -7.50000000000000007e-24

   1. Initial program 19.1%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 40.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.2%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 39.2%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 44.7%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 44.7%

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

   if -7.50000000000000007e-24 < y3 < 1.2000000000000001e-214

   1. Initial program 39.1%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 43.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 27.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 27.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(a \cdot \left(t \cdot z\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(0 - \color{blue}{a \cdot \left(t \cdot z\right)}\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(t \cdot z\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \left(z \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 25.2%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   11. Simplified 25.2%

       \[\leadsto b \cdot \color{blue}{\left(0 - a \cdot \left(z \cdot t\right)\right)} \]

   if 1.2000000000000001e-214 < y3 < 3.6999999999999998e-31

   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 y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 33.1%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 43.3%

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

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \color{blue}{\left(k \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 40.9%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{*.f64}\left(k, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 40.9%

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

   if 3.6999999999999998e-31 < y3 < 2.09999999999999992e127

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 40.2%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 34.4%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 34.4%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot x\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot a\right)\right), y\right) \]

       6. *-lowering-*.f64 37.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, a\right)\right), y\right) \]

   13. Applied egg-rr 37.3%

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

   if 2.09999999999999992e127 < y3

   1. Initial program 28.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 54.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.56 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.2 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(\left(z \cdot t\right) \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y3 \leq 3.7 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 21.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -2.25 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.1 \cdot 10^{-261}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 4.8 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.68e+218)
   (* (* a y3) (* z y1))
   (if (<= y3 -2.25e-60)
     (* c (* y (* y3 y4)))
     (if (<= y3 5.1e-261)
       (* k (* y1 (* y2 y4)))
       (if (<= y3 4.8e-31)
         (- 0.0 (* y0 (* y5 (* k y2))))
         (if (<= y3 4e+129) (* y (* b (* x a))) (* y4 (* c (* y y3)))))))))

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 <= -1.68e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -2.25e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 5.1e-261) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 4.8e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 4e+129) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.68d+218)) then
        tmp = (a * y3) * (z * y1)
    else if (y3 <= (-2.25d-60)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 5.1d-261) then
        tmp = k * (y1 * (y2 * y4))
    else if (y3 <= 4.8d-31) then
        tmp = 0.0d0 - (y0 * (y5 * (k * y2)))
    else if (y3 <= 4d+129) then
        tmp = y * (b * (x * a))
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.68e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -2.25e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 5.1e-261) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 4.8e-31) {
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	} else if (y3 <= 4e+129) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.68e+218:
		tmp = (a * y3) * (z * y1)
	elif y3 <= -2.25e-60:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 5.1e-261:
		tmp = k * (y1 * (y2 * y4))
	elif y3 <= 4.8e-31:
		tmp = 0.0 - (y0 * (y5 * (k * y2)))
	elif y3 <= 4e+129:
		tmp = y * (b * (x * a))
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.68e+218)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	elseif (y3 <= -2.25e-60)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 5.1e-261)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y3 <= 4.8e-31)
		tmp = Float64(0.0 - Float64(y0 * Float64(y5 * Float64(k * y2))));
	elseif (y3 <= 4e+129)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.68e+218)
		tmp = (a * y3) * (z * y1);
	elseif (y3 <= -2.25e-60)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 5.1e-261)
		tmp = k * (y1 * (y2 * y4));
	elseif (y3 <= 4.8e-31)
		tmp = 0.0 - (y0 * (y5 * (k * y2)));
	elseif (y3 <= 4e+129)
		tmp = y * (b * (x * a));
	else
		tmp = y4 * (c * (y * y3));
	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, -1.68e+218], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.25e-60], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.1e-261], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.8e-31], N[(0.0 - N[(y0 * N[(y5 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4e+129], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -1.6800000000000001e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 58.2%

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

   if -1.6800000000000001e218 < y3 < -2.25e-60

   1. Initial program 21.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 37.5%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 42.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 42.3%

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

   if -2.25e-60 < y3 < 5.09999999999999957e-261

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 37.7%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 28.1%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 28.1%

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

   9. Taylor expanded in y1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       4. *-lowering-*.f64 20.2%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 20.2%

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

   if 5.09999999999999957e-261 < y3 < 4.8e-31

   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 y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 34.8%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 34.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 34.9%

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

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \color{blue}{\left(k \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{*.f64}\left(k, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 35.0%

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

   if 4.8e-31 < y3 < 4e129

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 40.2%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 34.4%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 34.4%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot x\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot a\right)\right), y\right) \]

       6. *-lowering-*.f64 37.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, a\right)\right), y\right) \]

   13. Applied egg-rr 37.3%

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

   if 4e129 < y3

   1. Initial program 28.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 54.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -2.25 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.1 \cdot 10^{-261}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 4.8 \cdot 10^{-31}:\\ \;\;\;\;0 - y0 \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 4 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;y2 \leq -4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.85 \cdot 10^{+42}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - y4 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= y2 -4e+62)
     t_1
     (if (<= y2 -2.5e-208)
       (* z (- (* c (* t i)) (* k (- (* i y1) (* b y0)))))
       (if (<= y2 1.85e+42)
         (* y1 (- (* i (- (* x j) (* z k))) (* y4 (* j y3))))
         (if (<= y2 2.05e+211) (* 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -4e+62) {
		tmp = t_1;
	} else if (y2 <= -2.5e-208) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.85e+42) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	} else if (y2 <= 2.05e+211) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
    if (y2 <= (-4d+62)) then
        tmp = t_1
    else if (y2 <= (-2.5d-208)) then
        tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
    else if (y2 <= 1.85d+42) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)))
    else if (y2 <= 2.05d+211) then
        tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (y2 <= -4e+62) {
		tmp = t_1;
	} else if (y2 <= -2.5e-208) {
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.85e+42) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	} else if (y2 <= 2.05e+211) {
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if y2 <= -4e+62:
		tmp = t_1
	elif y2 <= -2.5e-208:
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))))
	elif y2 <= 1.85e+42:
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)))
	elif y2 <= 2.05e+211:
		tmp = 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(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (y2 <= -4e+62)
		tmp = t_1;
	elseif (y2 <= -2.5e-208)
		tmp = Float64(z * Float64(Float64(c * Float64(t * i)) - Float64(k * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 1.85e+42)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(y4 * Float64(j * y3))));
	elseif (y2 <= 2.05e+211)
		tmp = 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 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (y2 <= -4e+62)
		tmp = t_1;
	elseif (y2 <= -2.5e-208)
		tmp = z * ((c * (t * i)) - (k * ((i * y1) - (b * y0))));
	elseif (y2 <= 1.85e+42)
		tmp = y1 * ((i * ((x * j) - (z * k))) - (y4 * (j * y3)));
	elseif (y2 <= 2.05e+211)
		tmp = 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[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4e+62], t$95$1, If[LessEqual[y2, -2.5e-208], N[(z * N[(N[(c * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.85e+42], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.05e+211], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -4.00000000000000014e62 or 2.0499999999999999e211 < y2

   1. Initial program 17.7%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in y2 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y1\right)\right)} \]

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right), \left(\color{blue}{-1} \cdot y1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x + \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \left(a \cdot x - k \cdot y4\right)\right), \left(-1 \cdot y1\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(a \cdot x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(k \cdot y4\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(y4 \cdot k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(-1 \cdot y1\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(\mathsf{neg}\left(y1\right)\right)\right) \]

      15. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \left(0 - \color{blue}{y1}\right)\right) \]

      16. --lowering--.f64 54.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(y4, k\right)\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y1}\right)\right) \]

   8. Simplified 54.6%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - y4 \cdot k\right)\right) \cdot \left(0 - y1\right)} \]

   if -4.00000000000000014e62 < y2 < -2.49999999999999981e-208

   1. Initial program 32.1%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 38.2%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot t\right)\right)\right)}, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(\left(-1 \cdot c\right) \cdot \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{k}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \left(i \cdot t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 43.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, c\right), \mathsf{*.f64}\left(i, t\right)\right), \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, y1\right)\right)\right)\right)\right) \]

   8. Simplified 43.1%

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

   if -2.49999999999999981e-208 < y2 < 1.84999999999999998e42

   1. Initial program 36.6%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 47.4%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y2 around 0

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

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y1 \cdot \left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \color{blue}{\left(j \cdot \left(y3 \cdot y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \left(j \cdot \left(y3 \cdot y4\right) + \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(j \cdot \left(y3 \cdot y4\right)\right), \color{blue}{\left(\mathsf{neg}\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(j \cdot \left(y4 \cdot y3\right)\right), \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(\left(j \cdot y4\right) \cdot y3\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(\left(y4 \cdot j\right) \cdot y3\right), \left(\mathsf{neg}\left(\color{blue}{i} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\left(y4 \cdot \left(j \cdot y3\right)\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \left(j \cdot y3\right)\right), \left(\mathsf{neg}\left(\color{blue}{i \cdot \left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\mathsf{neg}\left(i \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right)\right) \]

       13. distribute-lft-neg-in N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right)\right) \]

       14. neg-mul-1 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\color{blue}{j \cdot x} - k \cdot z\right)\right)\right)\right)\right) \]

       15. sub-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(j \cdot x + \color{blue}{\left(\mathsf{neg}\left(k \cdot z\right)\right)}\right)\right)\right)\right)\right) \]

       16. +-commutative N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\left(\mathsf{neg}\left(k \cdot z\right)\right) + \color{blue}{j \cdot x}\right)\right)\right)\right)\right) \]

       17. distribute-lft-in N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(j, y3\right)\right), \left(\left(-1 \cdot i\right) \cdot \left(\mathsf{neg}\left(k \cdot z\right)\right) + \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot x\right)}\right)\right)\right)\right) \]

   11. Simplified 46.6%

       \[\leadsto \color{blue}{0 - y1 \cdot \left(y4 \cdot \left(j \cdot y3\right) + i \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 1.84999999999999998e42 < y2 < 2.0499999999999999e211

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 52.1%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 64.6%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4 \cdot 10^{+62}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i\right) - k \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.85 \cdot 10^{+42}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - y4 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.05 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 3900000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -8.2e+41)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -8.6e-126)
     (* y4 (* c (* y y3)))
     (if (<= a 3900000000.0)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= a 5.5e+77)
         (* (* a y3) (* z y1))
         (* y (* y5 (- (* i k) (* a y3)))))))))

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 (a <= -8.2e+41) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -8.6e-126) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 3900000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 5.5e+77) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	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 (a <= (-8.2d+41)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-8.6d-126)) then
        tmp = y4 * (c * (y * y3))
    else if (a <= 3900000000.0d0) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= 5.5d+77) then
        tmp = (a * y3) * (z * y1)
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    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 (a <= -8.2e+41) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -8.6e-126) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 3900000000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 5.5e+77) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -8.2e+41:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -8.6e-126:
		tmp = y4 * (c * (y * y3))
	elif a <= 3900000000.0:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= 5.5e+77:
		tmp = (a * y3) * (z * y1)
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	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 (a <= -8.2e+41)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -8.6e-126)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (a <= 3900000000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= 5.5e+77)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	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 (a <= -8.2e+41)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -8.6e-126)
		tmp = y4 * (c * (y * y3));
	elseif (a <= 3900000000.0)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= 5.5e+77)
		tmp = (a * y3) * (z * y1);
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	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[a, -8.2e+41], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.6e-126], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3900000000.0], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+77], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.2000000000000007e41

   1. Initial program 23.8%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -8.2000000000000007e41 < a < -8.60000000000000065e-126

   1. Initial program 37.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 33.4%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.6%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 38.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 38.7%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 38.7%

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

   if -8.60000000000000065e-126 < a < 3.9e9

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 35.7%

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

   if 3.9e9 < a < 5.50000000000000036e77

   1. Initial program 29.3%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 47.9%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 42.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 42.6%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 42.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 42.9%

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

   if 5.50000000000000036e77 < a

   1. Initial program 21.2%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 40.5%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 3900000000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -4.3 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.65e+218)
   (* (* a y3) (* z y1))
   (if (<= y3 -4.3e+48)
     (* c (* y (* y3 y4)))
     (if (<= y3 -4.8e-70)
       (* b (* a (- (* x y) (* z t))))
       (if (<= y3 1.7e+131)
         (* b (* j (- (* t y4) (* x y0))))
         (* y4 (* c (* y y3))))))))

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 <= -1.65e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -4.3e+48) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= -4.8e-70) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 1.7e+131) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.65d+218)) then
        tmp = (a * y3) * (z * y1)
    else if (y3 <= (-4.3d+48)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= (-4.8d-70)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y3 <= 1.7d+131) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.65e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -4.3e+48) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= -4.8e-70) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 1.7e+131) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.65e+218:
		tmp = (a * y3) * (z * y1)
	elif y3 <= -4.3e+48:
		tmp = c * (y * (y3 * y4))
	elif y3 <= -4.8e-70:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y3 <= 1.7e+131:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.65e+218)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	elseif (y3 <= -4.3e+48)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= -4.8e-70)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 1.7e+131)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.65e+218)
		tmp = (a * y3) * (z * y1);
	elseif (y3 <= -4.3e+48)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= -4.8e-70)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y3 <= 1.7e+131)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = y4 * (c * (y * y3));
	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, -1.65e+218], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.3e+48], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.8e-70], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.7e+131], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.64999999999999999e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 58.2%

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

   if -1.64999999999999999e218 < y3 < -4.29999999999999978e48

   1. Initial program 8.8%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.7%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 42.7%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 51.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 51.3%

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

   if -4.29999999999999978e48 < y3 < -4.8000000000000002e-70

   1. Initial program 40.4%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 47.8%

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

   if -4.8000000000000002e-70 < y3 < 1.69999999999999993e131

   1. Initial program 34.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 38.4%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(x \cdot y0\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\color{blue}{x} \cdot y0\right)\right)\right)\right) \]

      4. *-lowering-*.f64 30.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{*.f64}\left(x, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 30.9%

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

   if 1.69999999999999993e131 < y3

   1. Initial program 29.3%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 55.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 55.9%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 53.3%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 53.3%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -4.3 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 10200000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+215}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -9.5e+37)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -7e-126)
     (* y4 (* c (* y y3)))
     (if (<= a 10200000.0)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= a 1.65e+215) (* (* a y3) (* z y1)) (* y (* b (* x a))))))))

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 (a <= -9.5e+37) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7e-126) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 10200000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 1.65e+215) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (b * (x * a));
	}
	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 (a <= (-9.5d+37)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-7d-126)) then
        tmp = y4 * (c * (y * y3))
    else if (a <= 10200000.0d0) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= 1.65d+215) then
        tmp = (a * y3) * (z * y1)
    else
        tmp = y * (b * (x * a))
    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 (a <= -9.5e+37) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7e-126) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 10200000.0) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= 1.65e+215) {
		tmp = (a * y3) * (z * y1);
	} else {
		tmp = y * (b * (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -9.5e+37:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -7e-126:
		tmp = y4 * (c * (y * y3))
	elif a <= 10200000.0:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= 1.65e+215:
		tmp = (a * y3) * (z * y1)
	else:
		tmp = y * (b * (x * a))
	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 (a <= -9.5e+37)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -7e-126)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (a <= 10200000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= 1.65e+215)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	else
		tmp = Float64(y * Float64(b * Float64(x * a)));
	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 (a <= -9.5e+37)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -7e-126)
		tmp = y4 * (c * (y * y3));
	elseif (a <= 10200000.0)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= 1.65e+215)
		tmp = (a * y3) * (z * y1);
	else
		tmp = y * (b * (x * a));
	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[a, -9.5e+37], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-126], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 10200000.0], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+215], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.4999999999999995e37

   1. Initial program 23.8%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -9.4999999999999995e37 < a < -7e-126

   1. Initial program 37.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 33.4%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.6%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 38.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 38.7%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 38.7%

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

   if -7e-126 < a < 1.02e7

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.0%

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

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 35.7%

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

   if 1.02e7 < a < 1.6499999999999999e215

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 45.4%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 38.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 38.4%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 38.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 38.4%

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

   if 1.6499999999999999e215 < a

   1. Initial program 22.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 44.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 61.3%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 67.1%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 67.1%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot x\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot a\right)\right), y\right) \]

       6. *-lowering-*.f64 67.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, a\right)\right), y\right) \]

   13. Applied egg-rr 67.2%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-126}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 10200000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+215}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 8.8 \cdot 10^{-72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.65e+218)
   (* (* a y3) (* z y1))
   (if (<= y3 -1.12e-60)
     (* c (* y (* y3 y4)))
     (if (<= y3 8.8e-72)
       (* k (* y1 (* y2 y4)))
       (if (<= y3 2.1e+127) (* y (* b (* x a))) (* y4 (* c (* y y3))))))))

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 <= -1.65e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -1.12e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 8.8e-72) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.65d+218)) then
        tmp = (a * y3) * (z * y1)
    else if (y3 <= (-1.12d-60)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 8.8d-72) then
        tmp = k * (y1 * (y2 * y4))
    else if (y3 <= 2.1d+127) then
        tmp = y * (b * (x * a))
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.65e+218) {
		tmp = (a * y3) * (z * y1);
	} else if (y3 <= -1.12e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 8.8e-72) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.65e+218:
		tmp = (a * y3) * (z * y1)
	elif y3 <= -1.12e-60:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 8.8e-72:
		tmp = k * (y1 * (y2 * y4))
	elif y3 <= 2.1e+127:
		tmp = y * (b * (x * a))
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.65e+218)
		tmp = Float64(Float64(a * y3) * Float64(z * y1));
	elseif (y3 <= -1.12e-60)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 8.8e-72)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y3 <= 2.1e+127)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.65e+218)
		tmp = (a * y3) * (z * y1);
	elseif (y3 <= -1.12e-60)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 8.8e-72)
		tmp = k * (y1 * (y2 * y4));
	elseif (y3 <= 2.1e+127)
		tmp = y * (b * (x * a));
	else
		tmp = y4 * (c * (y * y3));
	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, -1.65e+218], N[(N[(a * y3), $MachinePrecision] * N[(z * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.12e-60], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8.8e-72], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e+127], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.64999999999999999e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \color{blue}{\left(a \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(y3 \cdot \color{blue}{a}\right)\right) \]

       2. *-lowering-*.f64 58.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y3, \color{blue}{a}\right)\right) \]

   11. Simplified 58.2%

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

   if -1.64999999999999999e218 < y3 < -1.12e-60

   1. Initial program 21.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 37.5%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 42.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 42.3%

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

   if -1.12e-60 < y3 < 8.8000000000000001e-72

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.2%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 30.6%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 30.6%

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

   9. Taylor expanded in y1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       4. *-lowering-*.f64 22.9%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 22.9%

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

   if 8.8000000000000001e-72 < y3 < 2.09999999999999992e127

   1. Initial program 25.5%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 37.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 35.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 31.7%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 31.7%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot x\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot a\right)\right), y\right) \]

       6. *-lowering-*.f64 33.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, a\right)\right), y\right) \]

   13. Applied egg-rr 33.9%

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

   if 2.09999999999999992e127 < y3

   1. Initial program 28.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 54.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+218}:\\ \;\;\;\;\left(a \cdot y3\right) \cdot \left(z \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 8.8 \cdot 10^{-72}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 6.4 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.68e+218)
   (* (* z y3) (* a y1))
   (if (<= y3 -1e-59)
     (* c (* y (* y3 y4)))
     (if (<= y3 6.4e-82)
       (* k (* y1 (* y2 y4)))
       (if (<= y3 2.1e+127) (* y (* b (* x a))) (* y4 (* c (* y y3))))))))

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 <= -1.68e+218) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= -1e-59) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 6.4e-82) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.68d+218)) then
        tmp = (z * y3) * (a * y1)
    else if (y3 <= (-1d-59)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 6.4d-82) then
        tmp = k * (y1 * (y2 * y4))
    else if (y3 <= 2.1d+127) then
        tmp = y * (b * (x * a))
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.68e+218) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= -1e-59) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 6.4e-82) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 2.1e+127) {
		tmp = y * (b * (x * a));
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.68e+218:
		tmp = (z * y3) * (a * y1)
	elif y3 <= -1e-59:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 6.4e-82:
		tmp = k * (y1 * (y2 * y4))
	elif y3 <= 2.1e+127:
		tmp = y * (b * (x * a))
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.68e+218)
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	elseif (y3 <= -1e-59)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 6.4e-82)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y3 <= 2.1e+127)
		tmp = Float64(y * Float64(b * Float64(x * a)));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.68e+218)
		tmp = (z * y3) * (a * y1);
	elseif (y3 <= -1e-59)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 6.4e-82)
		tmp = k * (y1 * (y2 * y4));
	elseif (y3 <= 2.1e+127)
		tmp = y * (b * (x * a));
	else
		tmp = y4 * (c * (y * y3));
	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, -1.68e+218], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1e-59], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.4e-82], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.1e+127], N[(y * N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.6800000000000001e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y1\right), \color{blue}{\left(y3 \cdot z\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y1\right), \left(\color{blue}{y3} \cdot z\right)\right) \]

       4. *-lowering-*.f64 53.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y1\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right) \]

   11. Simplified 53.1%

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

   if -1.6800000000000001e218 < y3 < -1e-59

   1. Initial program 21.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 37.5%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 42.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 42.3%

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

   if -1e-59 < y3 < 6.4000000000000002e-82

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.2%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 30.6%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 30.6%

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

   9. Taylor expanded in y1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       4. *-lowering-*.f64 22.9%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 22.9%

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

   if 6.4000000000000002e-82 < y3 < 2.09999999999999992e127

   1. Initial program 25.5%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 37.7%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 35.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 31.7%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 31.7%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(a \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot x\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot a\right)\right), y\right) \]

       6. *-lowering-*.f64 33.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, a\right)\right), y\right) \]

   13. Applied egg-rr 33.9%

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

   if 2.09999999999999992e127 < y3

   1. Initial program 28.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 54.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 6.4 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.8 \cdot 10^{+132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.68e+218)
   (* (* z y3) (* a y1))
   (if (<= y3 -3.8e-60)
     (* c (* y (* y3 y4)))
     (if (<= y3 2.6e-60)
       (* k (* y1 (* y2 y4)))
       (if (<= y3 5.8e+132) (* b (* (* x y) a)) (* y4 (* c (* y y3))))))))

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 <= -1.68e+218) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= -3.8e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 2.6e-60) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 5.8e+132) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= (-1.68d+218)) then
        tmp = (z * y3) * (a * y1)
    else if (y3 <= (-3.8d-60)) then
        tmp = c * (y * (y3 * y4))
    else if (y3 <= 2.6d-60) then
        tmp = k * (y1 * (y2 * y4))
    else if (y3 <= 5.8d+132) then
        tmp = b * ((x * y) * a)
    else
        tmp = y4 * (c * (y * y3))
    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 <= -1.68e+218) {
		tmp = (z * y3) * (a * y1);
	} else if (y3 <= -3.8e-60) {
		tmp = c * (y * (y3 * y4));
	} else if (y3 <= 2.6e-60) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y3 <= 5.8e+132) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = y4 * (c * (y * y3));
	}
	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 <= -1.68e+218:
		tmp = (z * y3) * (a * y1)
	elif y3 <= -3.8e-60:
		tmp = c * (y * (y3 * y4))
	elif y3 <= 2.6e-60:
		tmp = k * (y1 * (y2 * y4))
	elif y3 <= 5.8e+132:
		tmp = b * ((x * y) * a)
	else:
		tmp = y4 * (c * (y * y3))
	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 <= -1.68e+218)
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	elseif (y3 <= -3.8e-60)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y3 <= 2.6e-60)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y3 <= 5.8e+132)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	else
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	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 <= -1.68e+218)
		tmp = (z * y3) * (a * y1);
	elseif (y3 <= -3.8e-60)
		tmp = c * (y * (y3 * y4));
	elseif (y3 <= 2.6e-60)
		tmp = k * (y1 * (y2 * y4));
	elseif (y3 <= 5.8e+132)
		tmp = b * ((x * y) * a);
	else
		tmp = y4 * (c * (y * y3));
	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, -1.68e+218], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.8e-60], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.6e-60], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.8e+132], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.6800000000000001e218

   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 z around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 42.1%

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

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{a \cdot y3} - i \cdot k\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(i \cdot k\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{i} \cdot k\right)\right)\right) \]

      6. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{*.f64}\left(i, \color{blue}{k}\right)\right)\right) \]

   8. Simplified 58.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y1\right), \color{blue}{\left(y3 \cdot z\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y1\right), \left(\color{blue}{y3} \cdot z\right)\right) \]

       4. *-lowering-*.f64 53.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y1\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right) \]

   11. Simplified 53.1%

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

   if -1.6800000000000001e218 < y3 < -3.79999999999999994e-60

   1. Initial program 21.5%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 37.5%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 42.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 42.3%

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

   if -3.79999999999999994e-60 < y3 < 2.5999999999999998e-60

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 41.2%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 30.6%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 30.6%

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

   9. Taylor expanded in y1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       4. *-lowering-*.f64 22.9%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 22.9%

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

   if 2.5999999999999998e-60 < y3 < 5.7999999999999997e132

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 39.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 35.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 31.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 31.0%

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

   if 5.7999999999999997e132 < y3

   1. Initial program 29.3%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 55.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 55.9%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 53.3%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 53.3%

       \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.68 \cdot 10^{+218}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \mathbf{elif}\;y3 \leq -3.8 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.8 \cdot 10^{+132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 205000:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (* x y) a))))
   (if (<= a -1.7e+112)
     t_1
     (if (<= a -1.3e-124)
       (* y4 (* c (* y y3)))
       (if (<= a 205000.0)
         (* y1 (* k (* y2 y4)))
         (if (<= a 1.6e+214) (* j (* y3 (* y0 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -1.7e+112) {
		tmp = t_1;
	} else if (a <= -1.3e-124) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 205000.0) {
		tmp = y1 * (k * (y2 * y4));
	} else if (a <= 1.6e+214) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
    if (a <= (-1.7d+112)) then
        tmp = t_1
    else if (a <= (-1.3d-124)) then
        tmp = y4 * (c * (y * y3))
    else if (a <= 205000.0d0) then
        tmp = y1 * (k * (y2 * y4))
    else if (a <= 1.6d+214) then
        tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -1.7e+112) {
		tmp = t_1;
	} else if (a <= -1.3e-124) {
		tmp = y4 * (c * (y * y3));
	} else if (a <= 205000.0) {
		tmp = y1 * (k * (y2 * y4));
	} else if (a <= 1.6e+214) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
	tmp = 0
	if a <= -1.7e+112:
		tmp = t_1
	elif a <= -1.3e-124:
		tmp = y4 * (c * (y * y3))
	elif a <= 205000.0:
		tmp = y1 * (k * (y2 * y4))
	elif a <= 1.6e+214:
		tmp = j * (y3 * (y0 * 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(b * Float64(Float64(x * y) * a))
	tmp = 0.0
	if (a <= -1.7e+112)
		tmp = t_1;
	elseif (a <= -1.3e-124)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (a <= 205000.0)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (a <= 1.6e+214)
		tmp = Float64(j * Float64(y3 * Float64(y0 * 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 = b * ((x * y) * a);
	tmp = 0.0;
	if (a <= -1.7e+112)
		tmp = t_1;
	elseif (a <= -1.3e-124)
		tmp = y4 * (c * (y * y3));
	elseif (a <= 205000.0)
		tmp = y1 * (k * (y2 * y4));
	elseif (a <= 1.6e+214)
		tmp = j * (y3 * (y0 * 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[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+112], t$95$1, If[LessEqual[a, -1.3e-124], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 205000.0], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+214], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.69999999999999997e112 or 1.59999999999999997e214 < a

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 48.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 60.5%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 53.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 53.0%

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

   if -1.69999999999999997e112 < a < -1.3e-124

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 39.0%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 39.3%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \left(y3 \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 37.5%

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y3, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 37.5%

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

   if -1.3e-124 < a < 205000

   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 y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 38.1%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y2 around inf

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       7. *-lowering-*.f64 25.2%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 25.2%

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

   if 205000 < a < 1.59999999999999997e214

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 34.9%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 37.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 37.3%

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

   9. Taylor expanded in k around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(y3 \cdot y5\right) \cdot \color{blue}{y0}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \color{blue}{\left(y5 \cdot y0\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \color{blue}{\left(y0 \cdot y5\right)}\right)\right) \]

       6. *-lowering-*.f64 33.6%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \mathsf{*.f64}\left(y0, \color{blue}{y5}\right)\right)\right) \]

   11. Simplified 33.6%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 205000:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 20.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 260000:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (* x y) a))))
   (if (<= a -2.7e+110)
     t_1
     (if (<= a -1.2e-125)
       (* c (* y (* y3 y4)))
       (if (<= a 260000.0)
         (* y1 (* k (* y2 y4)))
         (if (<= a 1.45e+215) (* j (* y3 (* y0 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -2.7e+110) {
		tmp = t_1;
	} else if (a <= -1.2e-125) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 260000.0) {
		tmp = y1 * (k * (y2 * y4));
	} else if (a <= 1.45e+215) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
    if (a <= (-2.7d+110)) then
        tmp = t_1
    else if (a <= (-1.2d-125)) then
        tmp = c * (y * (y3 * y4))
    else if (a <= 260000.0d0) then
        tmp = y1 * (k * (y2 * y4))
    else if (a <= 1.45d+215) then
        tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -2.7e+110) {
		tmp = t_1;
	} else if (a <= -1.2e-125) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 260000.0) {
		tmp = y1 * (k * (y2 * y4));
	} else if (a <= 1.45e+215) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
	tmp = 0
	if a <= -2.7e+110:
		tmp = t_1
	elif a <= -1.2e-125:
		tmp = c * (y * (y3 * y4))
	elif a <= 260000.0:
		tmp = y1 * (k * (y2 * y4))
	elif a <= 1.45e+215:
		tmp = j * (y3 * (y0 * 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(b * Float64(Float64(x * y) * a))
	tmp = 0.0
	if (a <= -2.7e+110)
		tmp = t_1;
	elseif (a <= -1.2e-125)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (a <= 260000.0)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (a <= 1.45e+215)
		tmp = Float64(j * Float64(y3 * Float64(y0 * 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 = b * ((x * y) * a);
	tmp = 0.0;
	if (a <= -2.7e+110)
		tmp = t_1;
	elseif (a <= -1.2e-125)
		tmp = c * (y * (y3 * y4));
	elseif (a <= 260000.0)
		tmp = y1 * (k * (y2 * y4));
	elseif (a <= 1.45e+215)
		tmp = j * (y3 * (y0 * 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[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+110], t$95$1, If[LessEqual[a, -1.2e-125], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 260000.0], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+215], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7000000000000001e110 or 1.45e215 < a

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 48.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 60.5%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 53.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 53.0%

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

   if -2.7000000000000001e110 < a < -1.2000000000000001e-125

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 39.0%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 39.3%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 37.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 37.4%

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

   if -1.2000000000000001e-125 < a < 2.6e5

   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 y1 around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 38.1%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right), \color{blue}{\left(-1 \cdot y1\right)}\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(-y4\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(0 - y1\right)} \]

   9. Taylor expanded in y2 around inf

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       7. *-lowering-*.f64 25.2%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 25.2%

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

   if 2.6e5 < a < 1.45e215

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 34.9%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 37.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 37.3%

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

   9. Taylor expanded in k around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(y3 \cdot y5\right) \cdot \color{blue}{y0}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \color{blue}{\left(y5 \cdot y0\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \color{blue}{\left(y0 \cdot y5\right)}\right)\right) \]

       6. *-lowering-*.f64 33.6%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \mathsf{*.f64}\left(y0, \color{blue}{y5}\right)\right)\right) \]

   11. Simplified 33.6%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 260000:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* (* x y) a))))
   (if (<= a -3e+110)
     t_1
     (if (<= a -3.7e-124)
       (* c (* y (* y3 y4)))
       (if (<= a 1.05e-21)
         (* k (* y1 (* y2 y4)))
         (if (<= a 2.1e+214) (* j (* y3 (* y0 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -3e+110) {
		tmp = t_1;
	} else if (a <= -3.7e-124) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 1.05e-21) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 2.1e+214) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
    if (a <= (-3d+110)) then
        tmp = t_1
    else if (a <= (-3.7d-124)) then
        tmp = c * (y * (y3 * y4))
    else if (a <= 1.05d-21) then
        tmp = k * (y1 * (y2 * y4))
    else if (a <= 2.1d+214) then
        tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a);
	double tmp;
	if (a <= -3e+110) {
		tmp = t_1;
	} else if (a <= -3.7e-124) {
		tmp = c * (y * (y3 * y4));
	} else if (a <= 1.05e-21) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 2.1e+214) {
		tmp = j * (y3 * (y0 * 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 = b * ((x * y) * a)
	tmp = 0
	if a <= -3e+110:
		tmp = t_1
	elif a <= -3.7e-124:
		tmp = c * (y * (y3 * y4))
	elif a <= 1.05e-21:
		tmp = k * (y1 * (y2 * y4))
	elif a <= 2.1e+214:
		tmp = j * (y3 * (y0 * 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(b * Float64(Float64(x * y) * a))
	tmp = 0.0
	if (a <= -3e+110)
		tmp = t_1;
	elseif (a <= -3.7e-124)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (a <= 1.05e-21)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (a <= 2.1e+214)
		tmp = Float64(j * Float64(y3 * Float64(y0 * 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 = b * ((x * y) * a);
	tmp = 0.0;
	if (a <= -3e+110)
		tmp = t_1;
	elseif (a <= -3.7e-124)
		tmp = c * (y * (y3 * y4));
	elseif (a <= 1.05e-21)
		tmp = k * (y1 * (y2 * y4));
	elseif (a <= 2.1e+214)
		tmp = j * (y3 * (y0 * 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[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+110], t$95$1, If[LessEqual[a, -3.7e-124], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-21], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+214], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.00000000000000007e110 or 2.1000000000000001e214 < a

   1. Initial program 21.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 48.1%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 60.5%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 53.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 53.0%

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

   if -3.00000000000000007e110 < a < -3.6999999999999999e-124

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 39.0%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 39.3%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 37.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 37.4%

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

   if -3.6999999999999999e-124 < a < 1.05000000000000006e-21

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 43.0%

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

   6. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(k \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \left(y1 \cdot y2 + \color{blue}{-1 \cdot \left(b \cdot y\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(b \cdot y\right)\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1} \cdot \left(b \cdot y\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \color{blue}{\left(b \cdot y\right)}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(k, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{*.f64}\left(-1, \mathsf{*.f64}\left(b, \color{blue}{y}\right)\right)\right)\right)\right) \]

   8. Simplified 33.7%

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

   9. Taylor expanded in y1 around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(y1 \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \color{blue}{\left(y2 \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \left(y4 \cdot \color{blue}{y2}\right)\right)\right) \]

       4. *-lowering-*.f64 24.4%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 24.4%

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

   if 1.05000000000000006e-21 < a < 2.1000000000000001e214

   1. Initial program 24.7%

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

   3. Taylor expanded in y0 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c \cdot \left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(b \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 33.7%

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

   6. Taylor expanded in y5 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(-1 \cdot y5\right) \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      4. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(\color{blue}{k \cdot y2} - j \cdot y3\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 35.9%

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

   9. Taylor expanded in k around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(y3 \cdot y5\right) \cdot \color{blue}{y0}\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \color{blue}{\left(y5 \cdot y0\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(y3 \cdot \left(y0 \cdot \color{blue}{y5}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \color{blue}{\left(y0 \cdot y5\right)}\right)\right) \]

       6. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y3, \mathsf{*.f64}\left(y0, \color{blue}{y5}\right)\right)\right) \]

   11. Simplified 32.5%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-124}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 32.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.8e+44)
   (* b (* a (- (* x y) (* z t))))
   (if (<= a -7.5e-257)
     (* c (* y (- (* y3 y4) (* x i))))
     (if (<= a 2.4e+101)
       (* y4 (* y1 (- (* k y2) (* j y3))))
       (* y (* y5 (- (* i k) (* a y3))))))))

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 (a <= -1.8e+44) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7.5e-257) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 2.4e+101) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	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 (a <= (-1.8d+44)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (a <= (-7.5d-257)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= 2.4d+101) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    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 (a <= -1.8e+44) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (a <= -7.5e-257) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 2.4e+101) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -1.8e+44:
		tmp = b * (a * ((x * y) - (z * t)))
	elif a <= -7.5e-257:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= 2.4e+101:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	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 (a <= -1.8e+44)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (a <= -7.5e-257)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= 2.4e+101)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	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 (a <= -1.8e+44)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (a <= -7.5e-257)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= 2.4e+101)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	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[a, -1.8e+44], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-257], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+101], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.8e44

   1. Initial program 23.8%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 55.8%

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

   if -1.8e44 < a < -7.4999999999999995e-257

   1. Initial program 35.6%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 50.4%

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

   6. Taylor expanded in c around inf

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(c \cdot \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \left(y \cdot \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \left(i \cdot x - y3 \cdot y4\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(i \cdot x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(y3 \cdot y4\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y3, y4\right)\right)\right)\right)\right) \]

   8. Simplified 50.4%

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

   if -7.4999999999999995e-257 < a < 2.39999999999999988e101

   1. Initial program 32.9%

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

   3. Taylor expanded in y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 39.1%

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

   6. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \color{blue}{\left(k \cdot y2 - j \cdot y3\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \color{blue}{\left(j \cdot y3\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(\color{blue}{j} \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 36.3%

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

   if 2.39999999999999988e101 < a

   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 y around -inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y\right), \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y\right), \mathsf{\_.f64}\left(\left(-1 \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right) + k \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 41.8%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \color{blue}{\left(i \cdot k - a \cdot y3\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\left(i \cdot k\right), \color{blue}{\left(a \cdot y3\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \left(\color{blue}{a} \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y5, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, k\right), \mathsf{*.f64}\left(a, \color{blue}{y3}\right)\right)\right)\right) \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (* y3 y4)))))
   (if (<= y4 -3.55e-34) t_1 (if (<= y4 6.6e-24) (* b (* (* x y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -3.55e-34) {
		tmp = t_1;
	} else if (y4 <= 6.6e-24) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y * (y3 * y4))
    if (y4 <= (-3.55d-34)) then
        tmp = t_1
    else if (y4 <= 6.6d-24) then
        tmp = b * ((x * y) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -3.55e-34) {
		tmp = t_1;
	} else if (y4 <= 6.6e-24) {
		tmp = b * ((x * y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y * (y3 * y4))
	tmp = 0
	if y4 <= -3.55e-34:
		tmp = t_1
	elif y4 <= 6.6e-24:
		tmp = b * ((x * y) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(y3 * y4)))
	tmp = 0.0
	if (y4 <= -3.55e-34)
		tmp = t_1;
	elseif (y4 <= 6.6e-24)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * (y3 * y4));
	tmp = 0.0;
	if (y4 <= -3.55e-34)
		tmp = t_1;
	elseif (y4 <= 6.6e-24)
		tmp = b * ((x * y) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3.55e-34], t$95$1, If[LessEqual[y4, 6.6e-24], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y4 < -3.55000000000000018e-34 or 6.59999999999999968e-24 < y4

   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 y4 around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 50.7%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 35.8%

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 35.8%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y4 \cdot y3\right), y\right)\right) \]

       5. *-lowering-*.f64 35.8%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y4, y3\right), y\right)\right) \]

   11. Simplified 35.8%

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

   if -3.55000000000000018e-34 < y4 < 6.59999999999999968e-24

   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 b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 32.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 32.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 32.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 23.7%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 23.7%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(\left(x \cdot y\right) \cdot a\right) \end{array} \]

FPCore

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

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 b * ((x * y) * a);
}

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 = b * ((x * y) * a)
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 b * ((x * y) * a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

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

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

   15. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

5. Simplified 34.5%

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

6. Taylor expanded in a around inf

   \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

   4. *-lowering-*.f64 26.8%

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

8. Simplified 26.8%

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

9. Taylor expanded in x around inf

   \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

    2. *-lowering-*.f64 19.0%

       \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

11. Simplified 19.0%

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

12. Final simplification 19.0%

    \[\leadsto b \cdot \left(\left(x \cdot y\right) \cdot a\right) \]
13. Add Preprocessing

Developer Target 1: 27.8% 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 2024157 
(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
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* 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 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* 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 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* 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)))))