Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.9% → 41.2%

Time: 37.5s

Alternatives: 35

Speedup: 3.6×

• 89.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.9% 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: 41.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := y \cdot k - t \cdot j\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := y0 \cdot \left(y5 \cdot t\_3 - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_5 := i \cdot t\_2\\ \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+223}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{+142}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + t\_5\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot t\_1\\ \mathbf{elif}\;y5 \leq -4.7 \cdot 10^{-234}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t\_2 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(t\_5 + \left(a \cdot t\_1 + y0 \cdot t\_3\right)\right)\\ \end{array} \end{array} \]

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)))
        (t_2 (- (* y k) (* t j)))
        (t_3 (- (* j y3) (* k y2)))
        (t_4
         (*
          y0
          (-
           (* y5 t_3)
           (+ (* b (- (* x j) (* z k))) (* c (- (* z y3) (* x y2)))))))
        (t_5 (* i t_2)))
   (if (<= y5 -4.6e+223)
     t_4
     (if (<= y5 -3e+142)
       (* y5 (- (+ (* j (* y0 y3)) t_5) (* a (* y y3))))
       (if (<= y5 -4.1e+76)
         (* (* a y5) t_1)
         (if (<= y5 -4.7e-234)
           t_4
           (if (<= y5 8.6e-7)
             (*
              b
              (-
               (* y0 (- (* z k) (* x j)))
               (+ (* y4 t_2) (* a (- (* z t) (* x y))))))
             (* y5 (+ t_5 (+ (* a t_1) (* y0 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (y * k) - (t * j);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y0 * ((y5 * t_3) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	double t_5 = i * t_2;
	double tmp;
	if (y5 <= -4.6e+223) {
		tmp = t_4;
	} else if (y5 <= -3e+142) {
		tmp = y5 * (((j * (y0 * y3)) + t_5) - (a * (y * y3)));
	} else if (y5 <= -4.1e+76) {
		tmp = (a * y5) * t_1;
	} else if (y5 <= -4.7e-234) {
		tmp = t_4;
	} else if (y5 <= 8.6e-7) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	} else {
		tmp = y5 * (t_5 + ((a * t_1) + (y0 * t_3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (y * k) - (t * j)
    t_3 = (j * y3) - (k * y2)
    t_4 = y0 * ((y5 * t_3) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))))
    t_5 = i * t_2
    if (y5 <= (-4.6d+223)) then
        tmp = t_4
    else if (y5 <= (-3d+142)) then
        tmp = y5 * (((j * (y0 * y3)) + t_5) - (a * (y * y3)))
    else if (y5 <= (-4.1d+76)) then
        tmp = (a * y5) * t_1
    else if (y5 <= (-4.7d-234)) then
        tmp = t_4
    else if (y5 <= 8.6d-7) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))))
    else
        tmp = y5 * (t_5 + ((a * t_1) + (y0 * t_3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = (y * k) - (t * j);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y0 * ((y5 * t_3) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	double t_5 = i * t_2;
	double tmp;
	if (y5 <= -4.6e+223) {
		tmp = t_4;
	} else if (y5 <= -3e+142) {
		tmp = y5 * (((j * (y0 * y3)) + t_5) - (a * (y * y3)));
	} else if (y5 <= -4.1e+76) {
		tmp = (a * y5) * t_1;
	} else if (y5 <= -4.7e-234) {
		tmp = t_4;
	} else if (y5 <= 8.6e-7) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	} else {
		tmp = y5 * (t_5 + ((a * t_1) + (y0 * t_3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (y * k) - (t * j)
	t_3 = (j * y3) - (k * y2)
	t_4 = y0 * ((y5 * t_3) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))))
	t_5 = i * t_2
	tmp = 0
	if y5 <= -4.6e+223:
		tmp = t_4
	elif y5 <= -3e+142:
		tmp = y5 * (((j * (y0 * y3)) + t_5) - (a * (y * y3)))
	elif y5 <= -4.1e+76:
		tmp = (a * y5) * t_1
	elif y5 <= -4.7e-234:
		tmp = t_4
	elif y5 <= 8.6e-7:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))))
	else:
		tmp = y5 * (t_5 + ((a * t_1) + (y0 * t_3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(y0 * Float64(Float64(y5 * t_3) - Float64(Float64(b * Float64(Float64(x * j) - Float64(z * k))) + Float64(c * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_5 = Float64(i * t_2)
	tmp = 0.0
	if (y5 <= -4.6e+223)
		tmp = t_4;
	elseif (y5 <= -3e+142)
		tmp = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + t_5) - Float64(a * Float64(y * y3))));
	elseif (y5 <= -4.1e+76)
		tmp = Float64(Float64(a * y5) * t_1);
	elseif (y5 <= -4.7e-234)
		tmp = t_4;
	elseif (y5 <= 8.6e-7)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_2) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	else
		tmp = Float64(y5 * Float64(t_5 + Float64(Float64(a * t_1) + Float64(y0 * t_3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * y2) - (y * y3);
	t_2 = (y * k) - (t * j);
	t_3 = (j * y3) - (k * y2);
	t_4 = y0 * ((y5 * t_3) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	t_5 = i * t_2;
	tmp = 0.0;
	if (y5 <= -4.6e+223)
		tmp = t_4;
	elseif (y5 <= -3e+142)
		tmp = y5 * (((j * (y0 * y3)) + t_5) - (a * (y * y3)));
	elseif (y5 <= -4.1e+76)
		tmp = (a * y5) * t_1;
	elseif (y5 <= -4.7e-234)
		tmp = t_4;
	elseif (y5 <= 8.6e-7)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	else
		tmp = y5 * (t_5 + ((a * t_1) + (y0 * t_3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * N[(N[(y5 * t$95$3), $MachinePrecision] - N[(N[(b * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * t$95$2), $MachinePrecision]}, If[LessEqual[y5, -4.6e+223], t$95$4, If[LessEqual[y5, -3e+142], N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.1e+76], N[(N[(a * y5), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y5, -4.7e-234], t$95$4, If[LessEqual[y5, 8.6e-7], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$2), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(t$95$5 + N[(N[(a * t$95$1), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -4.60000000000000009e223 or -4.0999999999999998e76 < y5 < -4.7000000000000001e-234

   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 62.4%

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

   if -4.60000000000000009e223 < y5 < -2.99999999999999975e142

   1. Initial program 16.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.7%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 58.6%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if -2.99999999999999975e142 < y5 < -4.0999999999999998e76

   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 a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y5\right), \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right) \]

      6. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right) \]

   8. Simplified 80.0%

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

   if -4.7000000000000001e-234 < y5 < 8.6000000000000002e-7

   1. Initial program 30.6%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 51.2%

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

   if 8.6000000000000002e-7 < y5

   1. Initial program 26.7%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 56.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y5\right) \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right) + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+223}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{+142}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\\ \mathbf{elif}\;y5 \leq -4.7 \cdot 10^{-234}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 8.6 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * j) - (z * k)
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * t_1) + (c * ((z * y3) - (x * y2)))))
	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(x * j) - Float64(z * k))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(t_1 * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(c * y4) - Float64(a * y5)) * 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_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(Float64(b * t_1) + Float64(c * Float64(Float64(z * y3) - Float64(x * y2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * j) - (z * k);
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * t_1) + (c * ((z * y3) - (x * y2)))));
	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[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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[(t$95$1 * 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[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * 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$2, Infinity], t$95$2, N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * t$95$1), $MachinePrecision] + N[(c * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $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 88.6%

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

   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 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 41.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

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

Alternative 3: 39.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot t\_1\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-47}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.15 \cdot 10^{-83}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t\_1 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (* y5 (- (+ (* j (* y0 y3)) (* i t_1)) (* a (* y y3))))))
   (if (<= y5 -1.6e+148)
     t_2
     (if (<= y5 -2.4e+76)
       (* (* a y5) (- (* t y2) (* y y3)))
       (if (<= y5 -5e-47)
         (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (- (* x y2) (* z y3)))))
         (if (<= y5 -2.15e-83)
           (* (* x i) (* j y1))
           (if (<= y5 6e-201)
             (*
              x
              (+
               (* y (- (* a b) (* c i)))
               (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0))))))
             (if (<= y5 2.5e+15)
               (*
                b
                (-
                 (* y0 (- (* z k) (* x j)))
                 (+ (* y4 t_1) (* a (- (* z t) (* x y))))))
               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 = (y * k) - (t * j);
	double t_2 = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	double tmp;
	if (y5 <= -1.6e+148) {
		tmp = t_2;
	} else if (y5 <= -2.4e+76) {
		tmp = (a * y5) * ((t * y2) - (y * y3));
	} else if (y5 <= -5e-47) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	} else if (y5 <= -2.15e-83) {
		tmp = (x * i) * (j * y1);
	} else if (y5 <= 6e-201) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (y5 <= 2.5e+15) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	} 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 = (y * k) - (t * j)
    t_2 = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
    if (y5 <= (-1.6d+148)) then
        tmp = t_2
    else if (y5 <= (-2.4d+76)) then
        tmp = (a * y5) * ((t * y2) - (y * y3))
    else if (y5 <= (-5d-47)) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))))
    else if (y5 <= (-2.15d-83)) then
        tmp = (x * i) * (j * y1)
    else if (y5 <= 6d-201) then
        tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
    else if (y5 <= 2.5d+15) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
    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 = (y * k) - (t * j);
	double t_2 = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	double tmp;
	if (y5 <= -1.6e+148) {
		tmp = t_2;
	} else if (y5 <= -2.4e+76) {
		tmp = (a * y5) * ((t * y2) - (y * y3));
	} else if (y5 <= -5e-47) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	} else if (y5 <= -2.15e-83) {
		tmp = (x * i) * (j * y1);
	} else if (y5 <= 6e-201) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (y5 <= 2.5e+15) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	} 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 = (y * k) - (t * j)
	t_2 = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
	tmp = 0
	if y5 <= -1.6e+148:
		tmp = t_2
	elif y5 <= -2.4e+76:
		tmp = (a * y5) * ((t * y2) - (y * y3))
	elif y5 <= -5e-47:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))))
	elif y5 <= -2.15e-83:
		tmp = (x * i) * (j * y1)
	elif y5 <= 6e-201:
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
	elif y5 <= 2.5e+15:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
	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(y * k) - Float64(t * j))
	t_2 = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * t_1)) - Float64(a * Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -1.6e+148)
		tmp = t_2;
	elseif (y5 <= -2.4e+76)
		tmp = Float64(Float64(a * y5) * Float64(Float64(t * y2) - Float64(y * y3)));
	elseif (y5 <= -5e-47)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (y5 <= -2.15e-83)
		tmp = Float64(Float64(x * i) * Float64(j * y1));
	elseif (y5 <= 6e-201)
		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 * Float64(Float64(i * y1) - Float64(b * y0))))));
	elseif (y5 <= 2.5e+15)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	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 = (y * k) - (t * j);
	t_2 = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	tmp = 0.0;
	if (y5 <= -1.6e+148)
		tmp = t_2;
	elseif (y5 <= -2.4e+76)
		tmp = (a * y5) * ((t * y2) - (y * y3));
	elseif (y5 <= -5e-47)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	elseif (y5 <= -2.15e-83)
		tmp = (x * i) * (j * y1);
	elseif (y5 <= 6e-201)
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	elseif (y5 <= 2.5e+15)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	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[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.6e+148], t$95$2, If[LessEqual[y5, -2.4e+76], N[(N[(a * y5), $MachinePrecision] * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5e-47], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.15e-83], N[(N[(x * i), $MachinePrecision] * N[(j * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6e-201], 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 * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.5e+15], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.6e148 or 2.5e15 < y5

   1. Initial program 21.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 56.9%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if -1.6e148 < y5 < -2.4e76

   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 a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y5\right), \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right) \]

      6. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right) \]

   8. Simplified 80.0%

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

   if -2.4e76 < y5 < -5.00000000000000011e-47

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 67.4%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 56.3%

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

   8. Simplified 56.3%

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

   if -5.00000000000000011e-47 < y5 < -2.15000000000000017e-83

   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 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 33.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 52.5%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 52.5%

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

   9. Taylor expanded in c around 0

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \color{blue}{\left(-1 \cdot \left(j \cdot y1\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(\mathsf{neg}\left(j \cdot y1\right)\right)\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(\mathsf{neg}\left(y1 \cdot j\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(y1 \cdot \left(\mathsf{neg}\left(j\right)\right)\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(y1 \cdot \left(-1 \cdot j\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y1, \left(-1 \cdot j\right)\right)\right)\right) \]

       6. mul-1-neg N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y1, \left(\mathsf{neg}\left(j\right)\right)\right)\right)\right) \]

       7. neg-sub0 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y1, \left(0 - j\right)\right)\right)\right) \]

       8. --lowering--.f64 69.3%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(0, j\right)\right)\right)\right) \]

   11. Simplified 69.3%

       \[\leadsto -\left(i \cdot x\right) \cdot \color{blue}{\left(y1 \cdot \left(0 - j\right)\right)} \]

   if -2.15000000000000017e-83 < y5 < 6.00000000000000004e-201

   1. Initial program 43.1%

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

   3. Taylor expanded in 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 57.5%

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

   if 6.00000000000000004e-201 < y5 < 2.5e15

   1. Initial program 20.7%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 49.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-47}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.15 \cdot 10^{-83}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(j \cdot y1\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_2 := y \cdot k - t \cdot j\\ t_3 := y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot t\_2\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.26 \cdot 10^{+143}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot t\_2 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y0
          (-
           (* y5 (- (* j y3) (* k y2)))
           (+ (* b (- (* x j) (* z k))) (* c (- (* z y3) (* x y2)))))))
        (t_2 (- (* y k) (* t j)))
        (t_3 (* y5 (- (+ (* j (* y0 y3)) (* i t_2)) (* a (* y y3))))))
   (if (<= y5 -2e+224)
     t_1
     (if (<= y5 -1.26e+143)
       t_3
       (if (<= y5 -2.1e+76)
         (* (* a y5) (- (* t y2) (* y y3)))
         (if (<= y5 -9.5e-232)
           t_1
           (if (<= y5 3.8e+14)
             (*
              b
              (-
               (* y0 (- (* z k) (* x j)))
               (+ (* y4 t_2) (* a (- (* z t) (* x y))))))
             t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	double t_2 = (y * k) - (t * j);
	double t_3 = y5 * (((j * (y0 * y3)) + (i * t_2)) - (a * (y * y3)));
	double tmp;
	if (y5 <= -2e+224) {
		tmp = t_1;
	} else if (y5 <= -1.26e+143) {
		tmp = t_3;
	} else if (y5 <= -2.1e+76) {
		tmp = (a * y5) * ((t * y2) - (y * y3));
	} else if (y5 <= -9.5e-232) {
		tmp = t_1;
	} else if (y5 <= 3.8e+14) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))))
    t_2 = (y * k) - (t * j)
    t_3 = y5 * (((j * (y0 * y3)) + (i * t_2)) - (a * (y * y3)))
    if (y5 <= (-2d+224)) then
        tmp = t_1
    else if (y5 <= (-1.26d+143)) then
        tmp = t_3
    else if (y5 <= (-2.1d+76)) then
        tmp = (a * y5) * ((t * y2) - (y * y3))
    else if (y5 <= (-9.5d-232)) then
        tmp = t_1
    else if (y5 <= 3.8d+14) then
        tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	double t_2 = (y * k) - (t * j);
	double t_3 = y5 * (((j * (y0 * y3)) + (i * t_2)) - (a * (y * y3)));
	double tmp;
	if (y5 <= -2e+224) {
		tmp = t_1;
	} else if (y5 <= -1.26e+143) {
		tmp = t_3;
	} else if (y5 <= -2.1e+76) {
		tmp = (a * y5) * ((t * y2) - (y * y3));
	} else if (y5 <= -9.5e-232) {
		tmp = t_1;
	} else if (y5 <= 3.8e+14) {
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))))
	t_2 = (y * k) - (t * j)
	t_3 = y5 * (((j * (y0 * y3)) + (i * t_2)) - (a * (y * y3)))
	tmp = 0
	if y5 <= -2e+224:
		tmp = t_1
	elif y5 <= -1.26e+143:
		tmp = t_3
	elif y5 <= -2.1e+76:
		tmp = (a * y5) * ((t * y2) - (y * y3))
	elif y5 <= -9.5e-232:
		tmp = t_1
	elif y5 <= 3.8e+14:
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(Float64(b * Float64(Float64(x * j) - Float64(z * k))) + Float64(c * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * t_2)) - Float64(a * Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -2e+224)
		tmp = t_1;
	elseif (y5 <= -1.26e+143)
		tmp = t_3;
	elseif (y5 <= -2.1e+76)
		tmp = Float64(Float64(a * y5) * Float64(Float64(t * y2) - Float64(y * y3)));
	elseif (y5 <= -9.5e-232)
		tmp = t_1;
	elseif (y5 <= 3.8e+14)
		tmp = Float64(b * Float64(Float64(y0 * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y4 * t_2) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) - ((b * ((x * j) - (z * k))) + (c * ((z * y3) - (x * y2)))));
	t_2 = (y * k) - (t * j);
	t_3 = y5 * (((j * (y0 * y3)) + (i * t_2)) - (a * (y * y3)));
	tmp = 0.0;
	if (y5 <= -2e+224)
		tmp = t_1;
	elseif (y5 <= -1.26e+143)
		tmp = t_3;
	elseif (y5 <= -2.1e+76)
		tmp = (a * y5) * ((t * y2) - (y * y3));
	elseif (y5 <= -9.5e-232)
		tmp = t_1;
	elseif (y5 <= 3.8e+14)
		tmp = b * ((y0 * ((z * k) - (x * j))) - ((y4 * t_2) + (a * ((z * t) - (x * y)))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2e+224], t$95$1, If[LessEqual[y5, -1.26e+143], t$95$3, If[LessEqual[y5, -2.1e+76], N[(N[(a * y5), $MachinePrecision] * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.5e-232], t$95$1, If[LessEqual[y5, 3.8e+14], N[(b * N[(N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * t$95$2), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -1.99999999999999994e224 or -2.10000000000000007e76 < y5 < -9.50000000000000033e-232

   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 62.4%

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

   if -1.99999999999999994e224 < y5 < -1.2600000000000001e143 or 3.8e14 < y5

   1. Initial program 24.6%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 55.7%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 53.2%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if -1.2600000000000001e143 < y5 < -2.10000000000000007e76

   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 a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y5\right), \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \left(\color{blue}{t \cdot y2} - y \cdot y3\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right) \]

      6. *-lowering-*.f64 80.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right) \]

   8. Simplified 80.0%

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

   if -9.50000000000000033e-232 < y5 < 3.8e14

   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 50.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2 \cdot 10^{+224}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.26 \cdot 10^{+143}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -2.1 \cdot 10^{+76}:\\ \;\;\;\;\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)\\ \mathbf{elif}\;y5 \leq -9.5 \cdot 10^{-232}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) - \left(b \cdot \left(x \cdot j - z \cdot k\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := z \cdot k - x \cdot j\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;y0 \cdot \left(b \cdot t\_2\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-238}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot t\_1\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-60}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot t\_2 - \left(y4 \cdot t\_1 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j))) (t_2 (- (* z k) (* x j))))
   (if (<= b -1.45e+112)
     (* y0 (* b t_2))
     (if (<= b -1.25e+72)
       (* x (* y0 (- (* c y2) (* b j))))
       (if (<= b -1.1e-238)
         (* y5 (- (+ (* j (* y0 y3)) (* i t_1)) (* a (* y y3))))
         (if (<= b 1.15e-60)
           (*
            y2
            (+
             (* k (- (* y1 y4) (* y0 y5)))
             (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4))))))
           (if (<= b 2.5e+46)
             (*
              y4
              (+
               (* b (- (* t j) (* y k)))
               (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t y2))))))
             (*
              b
              (- (* y0 t_2) (+ (* y4 t_1) (* a (- (* z t) (* x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -1.45e+112) {
		tmp = y0 * (b * t_2);
	} else if (b <= -1.25e+72) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -1.1e-238) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 1.15e-60) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (b <= 2.5e+46) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (z * k) - (x * j)
    if (b <= (-1.45d+112)) then
        tmp = y0 * (b * t_2)
    else if (b <= (-1.25d+72)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-1.1d-238)) then
        tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
    else if (b <= 1.15d-60) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
    else if (b <= 2.5d+46) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
    else
        tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -1.45e+112) {
		tmp = y0 * (b * t_2);
	} else if (b <= -1.25e+72) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -1.1e-238) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 1.15e-60) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (b <= 2.5e+46) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (z * k) - (x * j)
	tmp = 0
	if b <= -1.45e+112:
		tmp = y0 * (b * t_2)
	elif b <= -1.25e+72:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -1.1e-238:
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
	elif b <= 1.15e-60:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
	elif b <= 2.5e+46:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
	else:
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	tmp = 0.0
	if (b <= -1.45e+112)
		tmp = Float64(y0 * Float64(b * t_2));
	elseif (b <= -1.25e+72)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -1.1e-238)
		tmp = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * t_1)) - Float64(a * Float64(y * y3))));
	elseif (b <= 1.15e-60)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (b <= 2.5e+46)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))));
	else
		tmp = Float64(b * Float64(Float64(y0 * t_2) - Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (z * k) - (x * j);
	tmp = 0.0;
	if (b <= -1.45e+112)
		tmp = y0 * (b * t_2);
	elseif (b <= -1.25e+72)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -1.1e-238)
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	elseif (b <= 1.15e-60)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	elseif (b <= 2.5e+46)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	else
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+112], N[(y0 * N[(b * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e+72], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-238], N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-60], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+46], N[(y4 * N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y0 * t$95$2), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.4500000000000001e112

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

   if -1.4500000000000001e112 < b < -1.24999999999999998e72

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 65.6%

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

   8. Simplified 65.6%

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

   if -1.24999999999999998e72 < b < -1.09999999999999996e-238

   1. Initial program 31.2%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 48.7%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if -1.09999999999999996e-238 < b < 1.1500000000000001e-60

   1. Initial program 32.4%

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

   3. Taylor expanded in 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 50.4%

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

   if 1.1500000000000001e-60 < b < 2.5000000000000001e46

   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 52.5%

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

   if 2.5000000000000001e46 < b

   1. Initial program 20.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 58.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-238}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-60}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := z \cdot k - x \cdot j\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot t\_2\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-267}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot t\_1\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 800000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot t\_2 - \left(y4 \cdot t\_1 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j))) (t_2 (- (* z k) (* x j))))
   (if (<= b -6.5e+109)
     (* y0 (* b t_2))
     (if (<= b -2.7e+70)
       (* x (* y0 (- (* c y2) (* b j))))
       (if (<= b 2.6e-267)
         (* y5 (- (+ (* j (* y0 y3)) (* i t_1)) (* a (* y y3))))
         (if (<= b 6.8e-56)
           (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
           (if (<= b 800000.0)
             (* (- (* k y2) (* j y3)) (* y1 y4))
             (*
              b
              (- (* y0 t_2) (+ (* y4 t_1) (* a (- (* z t) (* x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -6.5e+109) {
		tmp = y0 * (b * t_2);
	} else if (b <= -2.7e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= 2.6e-267) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 6.8e-56) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 800000.0) {
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (z * k) - (x * j)
    if (b <= (-6.5d+109)) then
        tmp = y0 * (b * t_2)
    else if (b <= (-2.7d+70)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= 2.6d-267) then
        tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
    else if (b <= 6.8d-56) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (b <= 800000.0d0) then
        tmp = ((k * y2) - (j * y3)) * (y1 * y4)
    else
        tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -6.5e+109) {
		tmp = y0 * (b * t_2);
	} else if (b <= -2.7e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= 2.6e-267) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 6.8e-56) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 800000.0) {
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (z * k) - (x * j)
	tmp = 0
	if b <= -6.5e+109:
		tmp = y0 * (b * t_2)
	elif b <= -2.7e+70:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= 2.6e-267:
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
	elif b <= 6.8e-56:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif b <= 800000.0:
		tmp = ((k * y2) - (j * y3)) * (y1 * y4)
	else:
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	tmp = 0.0
	if (b <= -6.5e+109)
		tmp = Float64(y0 * Float64(b * t_2));
	elseif (b <= -2.7e+70)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= 2.6e-267)
		tmp = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * t_1)) - Float64(a * Float64(y * y3))));
	elseif (b <= 6.8e-56)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= 800000.0)
		tmp = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(y1 * y4));
	else
		tmp = Float64(b * Float64(Float64(y0 * t_2) - Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (z * k) - (x * j);
	tmp = 0.0;
	if (b <= -6.5e+109)
		tmp = y0 * (b * t_2);
	elseif (b <= -2.7e+70)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= 2.6e-267)
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	elseif (b <= 6.8e-56)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= 800000.0)
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	else
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+109], N[(y0 * N[(b * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e+70], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-267], N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e-56], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 800000.0], N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y0 * t$95$2), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.5e109

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

   if -6.5e109 < b < -2.7e70

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 65.6%

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

   8. Simplified 65.6%

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

   if -2.7e70 < b < 2.6000000000000001e-267

   1. Initial program 32.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.0%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if 2.6000000000000001e-267 < b < 6.79999999999999964e-56

   1. Initial program 31.1%

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

   3. Taylor expanded in 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 57.9%

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

   6. Taylor expanded in k around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 57.9%

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

   8. Simplified 57.9%

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

   if 6.79999999999999964e-56 < b < 8e5

   1. Initial program 36.8%

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

   3. Taylor expanded in 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 53.2%

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

   6. Taylor expanded in y1 around inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      6. *-lowering-*.f64 43.6%

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

   8. Simplified 43.6%

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

   if 8e5 < b

   1. Initial program 23.2%

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

   3. Taylor expanded in 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 55.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-267}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 800000:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := z \cdot k - x \cdot j\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot t\_2\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-238}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot t\_1\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot t\_2 - \left(y4 \cdot t\_1 + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j))) (t_2 (- (* z k) (* x j))))
   (if (<= b -1.2e+109)
     (* y0 (* b t_2))
     (if (<= b -6.6e+70)
       (* x (* y0 (- (* c y2) (* b j))))
       (if (<= b -2.7e-238)
         (* y5 (- (+ (* j (* y0 y3)) (* i t_1)) (* a (* y y3))))
         (if (<= b 9.2e+128)
           (*
            y2
            (+
             (* k (- (* y1 y4) (* y0 y5)))
             (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4))))))
           (* b (- (* y0 t_2) (+ (* y4 t_1) (* a (- (* z t) (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -1.2e+109) {
		tmp = y0 * (b * t_2);
	} else if (b <= -6.6e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -2.7e-238) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 9.2e+128) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (z * k) - (x * j)
    if (b <= (-1.2d+109)) then
        tmp = y0 * (b * t_2)
    else if (b <= (-6.6d+70)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-2.7d-238)) then
        tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
    else if (b <= 9.2d+128) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
    else
        tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (z * k) - (x * j);
	double tmp;
	if (b <= -1.2e+109) {
		tmp = y0 * (b * t_2);
	} else if (b <= -6.6e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -2.7e-238) {
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	} else if (b <= 9.2e+128) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else {
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (z * k) - (x * j)
	tmp = 0
	if b <= -1.2e+109:
		tmp = y0 * (b * t_2)
	elif b <= -6.6e+70:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -2.7e-238:
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)))
	elif b <= 9.2e+128:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
	else:
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	tmp = 0.0
	if (b <= -1.2e+109)
		tmp = Float64(y0 * Float64(b * t_2));
	elseif (b <= -6.6e+70)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -2.7e-238)
		tmp = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * t_1)) - Float64(a * Float64(y * y3))));
	elseif (b <= 9.2e+128)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	else
		tmp = Float64(b * Float64(Float64(y0 * t_2) - Float64(Float64(y4 * t_1) + Float64(a * Float64(Float64(z * t) - Float64(x * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (z * k) - (x * j);
	tmp = 0.0;
	if (b <= -1.2e+109)
		tmp = y0 * (b * t_2);
	elseif (b <= -6.6e+70)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -2.7e-238)
		tmp = y5 * (((j * (y0 * y3)) + (i * t_1)) - (a * (y * y3)));
	elseif (b <= 9.2e+128)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	else
		tmp = b * ((y0 * t_2) - ((y4 * t_1) + (a * ((z * t) - (x * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+109], N[(y0 * N[(b * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e+70], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-238], N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+128], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y0 * t$95$2), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] + N[(a * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.19999999999999994e109

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

   if -1.19999999999999994e109 < b < -6.60000000000000033e70

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 65.6%

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

   8. Simplified 65.6%

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

   if -6.60000000000000033e70 < b < -2.69999999999999991e-238

   1. Initial program 31.2%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 48.7%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if -2.69999999999999991e-238 < b < 9.19999999999999992e128

   1. Initial program 32.3%

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

   3. Taylor expanded in 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 43.7%

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

   if 9.19999999999999992e128 < b

   1. Initial program 18.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 67.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-238}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right) - \left(y4 \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-266}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+84}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.6e+109)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -8e+71)
     (* x (* y0 (- (* c y2) (* b j))))
     (if (<= b 4.2e-266)
       (* y5 (- (+ (* j (* y0 y3)) (* i (- (* y k) (* t j)))) (* a (* y y3))))
       (if (<= b 1.85e+84)
         (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
         (if (<= b 1.12e+136)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (* b (* y4 (- (* t j) (* y 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 (b <= -1.6e+109) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -8e+71) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= 4.2e-266) {
		tmp = y5 * (((j * (y0 * y3)) + (i * ((y * k) - (t * j)))) - (a * (y * y3)));
	} else if (b <= 1.85e+84) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 1.12e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-1.6d+109)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-8d+71)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= 4.2d-266) then
        tmp = y5 * (((j * (y0 * y3)) + (i * ((y * k) - (t * j)))) - (a * (y * y3)))
    else if (b <= 1.85d+84) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (b <= 1.12d+136) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -1.6e+109) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -8e+71) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= 4.2e-266) {
		tmp = y5 * (((j * (y0 * y3)) + (i * ((y * k) - (t * j)))) - (a * (y * y3)));
	} else if (b <= 1.85e+84) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 1.12e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -1.6e+109:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -8e+71:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= 4.2e-266:
		tmp = y5 * (((j * (y0 * y3)) + (i * ((y * k) - (t * j)))) - (a * (y * y3)))
	elif b <= 1.85e+84:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif b <= 1.12e+136:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -1.6e+109)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -8e+71)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= 4.2e-266)
		tmp = Float64(y5 * Float64(Float64(Float64(j * Float64(y0 * y3)) + Float64(i * Float64(Float64(y * k) - Float64(t * j)))) - Float64(a * Float64(y * y3))));
	elseif (b <= 1.85e+84)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= 1.12e+136)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -1.6e+109)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -8e+71)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= 4.2e-266)
		tmp = y5 * (((j * (y0 * y3)) + (i * ((y * k) - (t * j)))) - (a * (y * y3)));
	elseif (b <= 1.85e+84)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= 1.12e+136)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -1.6e+109], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e+71], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-266], N[(y5 * N[(N[(N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+84], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+136], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.6000000000000001e109

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

   if -1.6000000000000001e109 < b < -8.0000000000000003e71

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 65.6%

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

   8. Simplified 65.6%

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

   if -8.0000000000000003e71 < b < 4.19999999999999994e-266

   1. Initial program 32.3%

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

   3. Taylor expanded in y5 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y5\right), \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(\color{blue}{\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \left(i \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\left(i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y0 \cdot \left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y0 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y5\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.0%

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

   6. Taylor expanded in y2 around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(y5 \cdot \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) - -1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \mathsf{+.f64}\left(\left(-1 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right) + i \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot \left(y \cdot y3\right)\right)\right)\right)}\right)\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{0 - y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) - j \cdot \left(y0 \cdot y3\right)\right) + a \cdot \left(y \cdot y3\right)\right)} \]

   if 4.19999999999999994e-266 < b < 1.85e84

   1. Initial program 32.6%

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

   3. Taylor expanded in 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 45.0%

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

   6. Taylor expanded in k around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 45.1%

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

   8. Simplified 45.1%

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

   if 1.85e84 < b < 1.12000000000000001e136

   1. Initial program 20.0%

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

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 60.0%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 70.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 70.3%

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

   if 1.12000000000000001e136 < b

   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 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 69.5%

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

   6. Taylor expanded in 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 53.5%

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

   8. Simplified 53.5%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+109}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-266}:\\ \;\;\;\;y5 \cdot \left(\left(j \cdot \left(y0 \cdot y3\right) + i \cdot \left(y \cdot k - t \cdot j\right)\right) - a \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+84}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.86 \cdot 10^{-199}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-268}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+84}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+133}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2.55e+113)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -1.86e-199)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= b 3.2e-268)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= b 1.65e+84)
         (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
         (if (<= b 1.08e+133)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (* b (* y4 (- (* t j) (* y 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 (b <= -2.55e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.86e-199) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 3.2e-268) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 1.65e+84) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 1.08e+133) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-2.55d+113)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-1.86d-199)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 3.2d-268) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (b <= 1.65d+84) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (b <= 1.08d+133) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.55e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.86e-199) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 3.2e-268) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 1.65e+84) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 1.08e+133) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -2.55e+113:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -1.86e-199:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 3.2e-268:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif b <= 1.65e+84:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif b <= 1.08e+133:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.55e+113)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1.86e-199)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 3.2e-268)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (b <= 1.65e+84)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= 1.08e+133)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -2.55e+113)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -1.86e-199)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 3.2e-268)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (b <= 1.65e+84)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (b <= 1.08e+133)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -2.55e+113], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.86e-199], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-268], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e+84], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.08e+133], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.54999999999999997e113

   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 53.7%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 63.0%

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

   8. Simplified 63.0%

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

   if -2.54999999999999997e113 < b < -1.85999999999999993e-199

   1. Initial program 29.8%

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

   3. Taylor expanded in 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 b around 0

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 36.1%

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

   8. Simplified 36.1%

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

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(j \cdot y5\right), \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y5 \cdot j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 41.6%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 41.6%

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

   if -1.85999999999999993e-199 < b < 3.1999999999999999e-268

   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 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 41.3%

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

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

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

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

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

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

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

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

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

      5. *-lowering-*.f64 41.9%

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

   8. Simplified 41.9%

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

   if 3.1999999999999999e-268 < b < 1.65000000000000008e84

   1. Initial program 32.6%

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

   3. Taylor expanded in 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 45.0%

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

   6. Taylor expanded in k around 0

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 45.1%

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

   8. Simplified 45.1%

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

   if 1.65000000000000008e84 < b < 1.08e133

   1. Initial program 20.0%

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

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 60.0%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 70.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 70.3%

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

   if 1.08e133 < b

   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 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 69.5%

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

   6. Taylor expanded in 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 53.5%

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

   8. Simplified 53.5%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.86 \cdot 10^{-199}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-268}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+84}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+133}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-129}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+73}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+158}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2.5e+113)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -2.85e-204)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= b 2.8e-129)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (if (<= b 1.14e+73)
         (* y4 (* c (- (* y y3) (* t y2))))
         (if (<= b 2.6e+158)
           (* (- (* k y2) (* j y3)) (* y1 y4))
           (* b (* y4 (- (* t j) (* y 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 (b <= -2.5e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2.85e-204) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2.8e-129) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.14e+73) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 2.6e+158) {
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-2.5d+113)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-2.85d-204)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 2.8d-129) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 1.14d+73) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (b <= 2.6d+158) then
        tmp = ((k * y2) - (j * y3)) * (y1 * y4)
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.5e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2.85e-204) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2.8e-129) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.14e+73) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 2.6e+158) {
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -2.5e+113:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -2.85e-204:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 2.8e-129:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 1.14e+73:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif b <= 2.6e+158:
		tmp = ((k * y2) - (j * y3)) * (y1 * y4)
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.5e+113)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -2.85e-204)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 2.8e-129)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 1.14e+73)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 2.6e+158)
		tmp = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(y1 * y4));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -2.5e+113)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -2.85e-204)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 2.8e-129)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 1.14e+73)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (b <= 2.6e+158)
		tmp = ((k * y2) - (j * y3)) * (y1 * y4);
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -2.5e+113], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.85e-204], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-129], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.14e+73], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+158], N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(y1 * y4), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.5e113

   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 53.7%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 63.0%

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

   8. Simplified 63.0%

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

   if -2.5e113 < b < -2.85e-204

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 38.4%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 38.3%

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

   8. Simplified 38.3%

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

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(j \cdot y5\right), \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y5 \cdot j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 42.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 42.0%

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

   if -2.85e-204 < b < 2.7999999999999999e-129

   1. Initial program 35.5%

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

   3. Taylor expanded in 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 44.5%

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

   6. Taylor expanded in y1 around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 45.0%

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

   8. Simplified 45.0%

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

   if 2.7999999999999999e-129 < b < 1.1399999999999999e73

   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 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 43.9%

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

   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%

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

   if 1.1399999999999999e73 < b < 2.6e158

   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 42.0%

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

   6. Taylor expanded in y1 around inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      6. *-lowering-*.f64 59.3%

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

   8. Simplified 59.3%

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

   if 2.6e158 < b

   1. Initial program 15.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 65.7%

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

   6. Taylor expanded in 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 53.9%

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

   8. Simplified 53.9%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-129}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+73}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+158}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-129}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+138}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -3e+113)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -2.8e-203)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= b 2e-129)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (if (<= b 3.4e+84)
         (* y4 (* c (- (* y y3) (* t y2))))
         (if (<= b 1.1e+138)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (* b (* y4 (- (* t j) (* y 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 (b <= -3e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2.8e-203) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2e-129) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 3.4e+84) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 1.1e+138) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-3d+113)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-2.8d-203)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 2d-129) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 3.4d+84) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (b <= 1.1d+138) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -3e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2.8e-203) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2e-129) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 3.4e+84) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 1.1e+138) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -3e+113:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -2.8e-203:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 2e-129:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 3.4e+84:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif b <= 1.1e+138:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -3e+113)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -2.8e-203)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 2e-129)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 3.4e+84)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 1.1e+138)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -3e+113)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -2.8e-203)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 2e-129)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 3.4e+84)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (b <= 1.1e+138)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -3e+113], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-203], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-129], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+84], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+138], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3e113

   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 53.7%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 63.0%

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

   8. Simplified 63.0%

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

   if -3e113 < b < -2.80000000000000022e-203

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 38.4%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 38.3%

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

   8. Simplified 38.3%

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

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(j \cdot y5\right), \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y5 \cdot j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 42.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 42.0%

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

   if -2.80000000000000022e-203 < b < 1.9999999999999999e-129

   1. Initial program 35.5%

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

   3. Taylor expanded in 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 44.5%

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

   6. Taylor expanded in y1 around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 45.0%

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

   8. Simplified 45.0%

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

   if 1.9999999999999999e-129 < b < 3.3999999999999998e84

   1. Initial program 31.6%

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

   3. Taylor expanded in 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 43.4%

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

   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 38.4%

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

   8. Simplified 38.4%

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

   if 3.3999999999999998e84 < b < 1.1e138

   1. Initial program 20.0%

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

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 60.0%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 70.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 70.3%

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

   if 1.1e138 < b

   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 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 69.5%

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

   6. Taylor expanded in 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 53.5%

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

   8. Simplified 53.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-129}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+138}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+111}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-84}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -7e+111)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -1.2e+70)
     (* x (* y0 (- (* c y2) (* b j))))
     (if (<= b -7.4e-84)
       (- 0.0 (* a (* y3 (* y y5))))
       (if (<= b 1.6e+88)
         (* i (* z (- (* t c) (* k y1))))
         (if (<= b 3.8e+136)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (* b (* y4 (- (* t j) (* y 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 (b <= -7e+111) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.2e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -7.4e-84) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 1.6e+88) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 3.8e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-7d+111)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-1.2d+70)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-7.4d-84)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 1.6d+88) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (b <= 3.8d+136) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -7e+111) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.2e+70) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -7.4e-84) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 1.6e+88) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 3.8e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -7e+111:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -1.2e+70:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -7.4e-84:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 1.6e+88:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif b <= 3.8e+136:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -7e+111)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1.2e+70)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -7.4e-84)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 1.6e+88)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (b <= 3.8e+136)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -7e+111)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -1.2e+70)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -7.4e-84)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 1.6e+88)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (b <= 3.8e+136)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -7e+111], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e+70], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.4e-84], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+88], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+136], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7.0000000000000004e111

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 61.6%

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

   8. Simplified 61.6%

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

   if -7.0000000000000004e111 < b < -1.19999999999999993e70

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 65.6%

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

   8. Simplified 65.6%

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

   if -1.19999999999999993e70 < b < -7.3999999999999999e-84

   1. Initial program 26.5%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 48.4%

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

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 31.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 31.5%

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

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 44.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 44.8%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -7.3999999999999999e-84 < b < 1.5999999999999999e88

   1. Initial program 33.0%

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

   3. Taylor expanded in 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 30.8%

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

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

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

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

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

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

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

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

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

      5. *-lowering-*.f64 32.0%

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

   8. Simplified 32.0%

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

   if 1.5999999999999999e88 < b < 3.80000000000000015e136

   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 62.5%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 75.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 75.1%

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

   if 3.80000000000000015e136 < b

   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 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 69.5%

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

   6. Taylor expanded in 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 53.5%

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

   8. Simplified 53.5%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+111}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-84}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6.6 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -2.35e+115)
   (* b (* y4 (- (* t j) (* y k))))
   (if (<= y4 -1.9e+29)
     (* b (* a (- (* x y) (* z t))))
     (if (<= y4 -1.02e-30)
       (* x (* y0 (- (* c y2) (* b j))))
       (if (<= y4 1.5e-293)
         (* a (* y3 (- (* z y1) (* y y5))))
         (if (<= y4 6.6e+92)
           (* i (* z (- (* t c) (* k y1))))
           (* t (* y4 (- (* b j) (* c y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -2.35e+115) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.9e+29) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= -1.02e-30) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y4 <= 1.5e-293) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 6.6e+92) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-2.35d+115)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.9d+29)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y4 <= (-1.02d-30)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y4 <= 1.5d-293) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y4 <= 6.6d+92) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = t * (y4 * ((b * j) - (c * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -2.35e+115) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.9e+29) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= -1.02e-30) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y4 <= 1.5e-293) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 6.6e+92) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -2.35e+115:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.9e+29:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y4 <= -1.02e-30:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y4 <= 1.5e-293:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y4 <= 6.6e+92:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -2.35e+115)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.9e+29)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= -1.02e-30)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y4 <= 1.5e-293)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y4 <= 6.6e+92)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -2.35e+115)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.9e+29)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y4 <= -1.02e-30)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y4 <= 1.5e-293)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y4 <= 6.6e+92)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = t * (y4 * ((b * j) - (c * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -2.35e+115], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.9e+29], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.02e-30], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.5e-293], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.6e+92], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -2.3499999999999998e115

   1. Initial program 6.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.4%

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

   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 53.4%

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

   8. Simplified 53.4%

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

   if -2.3499999999999998e115 < y4 < -1.89999999999999985e29

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 50.3%

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

   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 56.4%

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

   8. Simplified 56.4%

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

   if -1.89999999999999985e29 < y4 < -1.0199999999999999e-30

   1. Initial program 44.1%

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

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 56.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 63.0%

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

   8. Simplified 63.0%

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

   if -1.0199999999999999e-30 < y4 < 1.5000000000000001e-293

   1. Initial program 39.0%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 45.3%

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

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.1%

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

   if 1.5000000000000001e-293 < y4 < 6.59999999999999948e92

   1. Initial program 27.6%

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

   3. Taylor expanded in 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 37.2%

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

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

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

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

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

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

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

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

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

      5. *-lowering-*.f64 36.4%

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

   8. Simplified 36.4%

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

   if 6.59999999999999948e92 < y4

   1. Initial program 19.5%

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

   3. Taylor expanded in 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 58.7%

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

   6. Taylor expanded in t around inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 49.2%

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

   8. Simplified 49.2%

      \[\leadsto \color{blue}{t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.35 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 6.6 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-248}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-26}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+247}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(0 - j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -5.2e+71)
   (* y0 (* b (* z k)))
   (if (<= b -6.8e-248)
     (- 0.0 (* a (* y3 (* y y5))))
     (if (<= b 6.5e-26)
       (* k (- 0.0 (* y0 (* y2 y5))))
       (if (<= b 9.5e+83)
         (* y1 (* a (* z y3)))
         (if (<= b 3.3e+247)
           (* y0 (* b (* x (- 0.0 j))))
           (* b (* z (* k y0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5.2e+71) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -6.8e-248) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 6.5e-26) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else if (b <= 9.5e+83) {
		tmp = y1 * (a * (z * y3));
	} else if (b <= 3.3e+247) {
		tmp = y0 * (b * (x * (0.0 - j)));
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-5.2d+71)) then
        tmp = y0 * (b * (z * k))
    else if (b <= (-6.8d-248)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 6.5d-26) then
        tmp = k * (0.0d0 - (y0 * (y2 * y5)))
    else if (b <= 9.5d+83) then
        tmp = y1 * (a * (z * y3))
    else if (b <= 3.3d+247) then
        tmp = y0 * (b * (x * (0.0d0 - j)))
    else
        tmp = b * (z * (k * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -5.2e+71) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -6.8e-248) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 6.5e-26) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else if (b <= 9.5e+83) {
		tmp = y1 * (a * (z * y3));
	} else if (b <= 3.3e+247) {
		tmp = y0 * (b * (x * (0.0 - j)));
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -5.2e+71:
		tmp = y0 * (b * (z * k))
	elif b <= -6.8e-248:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 6.5e-26:
		tmp = k * (0.0 - (y0 * (y2 * y5)))
	elif b <= 9.5e+83:
		tmp = y1 * (a * (z * y3))
	elif b <= 3.3e+247:
		tmp = y0 * (b * (x * (0.0 - j)))
	else:
		tmp = b * (z * (k * y0))
	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 (b <= -5.2e+71)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (b <= -6.8e-248)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 6.5e-26)
		tmp = Float64(k * Float64(0.0 - Float64(y0 * Float64(y2 * y5))));
	elseif (b <= 9.5e+83)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	elseif (b <= 3.3e+247)
		tmp = Float64(y0 * Float64(b * Float64(x * Float64(0.0 - j))));
	else
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -5.2e+71)
		tmp = y0 * (b * (z * k));
	elseif (b <= -6.8e-248)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 6.5e-26)
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	elseif (b <= 9.5e+83)
		tmp = y1 * (a * (z * y3));
	elseif (b <= 3.3e+247)
		tmp = y0 * (b * (x * (0.0 - j)));
	else
		tmp = b * (z * (k * y0));
	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[b, -5.2e+71], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.8e-248], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-26], N[(k * N[(0.0 - N[(y0 * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+83], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+247], N[(y0 * N[(b * N[(x * N[(0.0 - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.19999999999999983e71

   1. Initial program 15.5%

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

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 50.2%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in k around inf

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

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

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

       2. *-lowering-*.f64 42.1%

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

   11. Simplified 42.1%

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

   if -5.19999999999999983e71 < b < -6.7999999999999996e-248

   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 a around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.3%

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

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.5%

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

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 34.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 34.7%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -6.7999999999999996e-248 < b < 6.5e-26

   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 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 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 35.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto k \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto k \cdot \left(-1 \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(0 - \color{blue}{y0 \cdot \left(y2 \cdot y5\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \left(y5 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 29.8%

           \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y5, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 29.8%

       \[\leadsto \color{blue}{k \cdot \left(0 - y0 \cdot \left(y5 \cdot y2\right)\right)} \]

   if 6.5e-26 < b < 9.5000000000000002e83

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 21.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 21.0%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 21.1%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 21.1%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(\left(y3 \cdot z\right) \cdot \color{blue}{y1}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(y3 \cdot z\right)\right) \cdot \color{blue}{y1} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(y3 \cdot z\right)\right), \color{blue}{y1}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(y3 \cdot z\right)\right), y1\right) \]

       5. *-lowering-*.f64 27.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, z\right)\right), y1\right) \]

   13. Applied egg-rr 27.3%

       \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

   if 9.5000000000000002e83 < b < 3.30000000000000001e247

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 40.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 34.2%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 34.2%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(\mathsf{neg}\left(b \cdot \left(j \cdot x\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(0 - \color{blue}{b \cdot \left(j \cdot x\right)}\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(0, \color{blue}{\left(b \cdot \left(j \cdot x\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(b, \left(x \cdot \color{blue}{j}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 37.7%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{j}\right)\right)\right)\right) \]

   11. Simplified 37.7%

       \[\leadsto y0 \cdot \color{blue}{\left(0 - b \cdot \left(x \cdot j\right)\right)} \]

   if 3.30000000000000001e247 < b

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 45.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 45.0%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-248}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-26}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+247}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(0 - j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.1% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-196}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2.15e+113)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -2e-196)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= b 2.55e+88)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= b 4.1e+136)
         (* y0 (* j (- (* y3 y5) (* x b))))
         (* b (* y4 (- (* t j) (* y 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 (b <= -2.15e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2e-196) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2.55e+88) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 4.1e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-2.15d+113)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-2d-196)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 2.55d+88) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (b <= 4.1d+136) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.15e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -2e-196) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 2.55e+88) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (b <= 4.1e+136) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -2.15e+113:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -2e-196:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 2.55e+88:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif b <= 4.1e+136:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -2.15e+113)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -2e-196)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 2.55e+88)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (b <= 4.1e+136)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -2.15e+113)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -2e-196)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 2.55e+88)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (b <= 4.1e+136)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -2.15e+113], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-196], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+88], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+136], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.1500000000000002e113

   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 53.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 63.0%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -2.1500000000000002e113 < b < -2.0000000000000001e-196

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 36.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)}\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \color{blue}{-1 \cdot \left(c \cdot z\right)}\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 - \color{blue}{c \cdot z}\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(j \cdot y5\right), \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y5 \cdot j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 41.6%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 41.6%

       \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot j - z \cdot c\right)\right)} \]

   if -2.0000000000000001e-196 < b < 2.5499999999999999e88

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 29.8%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right)\right) \]

   8. Simplified 32.7%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 2.5499999999999999e88 < b < 4.0999999999999998e136

   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 62.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 75.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 75.1%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   if 4.0999999999999998e136 < b

   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 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 69.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 53.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-196}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+245}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= t -8.2e+54)
     (* i (* z (- (* t c) (* k y1))))
     (if (<= t 8e-248)
       t_1
       (if (<= t 4.5e+96)
         (* y0 (* c (- (* x y2) (* z y3))))
         (if (<= t 8e+245) (* b (* a (- (* x y) (* z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (t <= -8.2e+54) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (t <= 8e-248) {
		tmp = t_1;
	} else if (t <= 4.5e+96) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= 8e+245) {
		tmp = b * (a * ((x * y) - (z * t)));
	} 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 = y0 * (b * ((z * k) - (x * j)))
    if (t <= (-8.2d+54)) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (t <= 8d-248) then
        tmp = t_1
    else if (t <= 4.5d+96) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (t <= 8d+245) then
        tmp = b * (a * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (t <= -8.2e+54) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (t <= 8e-248) {
		tmp = t_1;
	} else if (t <= 4.5e+96) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= 8e+245) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if t <= -8.2e+54:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif t <= 8e-248:
		tmp = t_1
	elif t <= 4.5e+96:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif t <= 8e+245:
		tmp = b * (a * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (t <= -8.2e+54)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (t <= 8e-248)
		tmp = t_1;
	elseif (t <= 4.5e+96)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= 8e+245)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (t <= -8.2e+54)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (t <= 8e-248)
		tmp = t_1;
	elseif (t <= 4.5e+96)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (t <= 8e+245)
		tmp = b * (a * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+54], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-248], t$95$1, If[LessEqual[t, 4.5e+96], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+245], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.19999999999999935e54

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 40.9%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 46.3%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right)\right) \]

   8. Simplified 46.3%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if -8.19999999999999935e54 < t < 7.99999999999999984e-248 or 8.00000000000000035e245 < t

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 49.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 7.99999999999999984e-248 < t < 4.49999999999999957e96

   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 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 46.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   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 37.4%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 37.4%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 4.49999999999999957e96 < t < 8.00000000000000035e245

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 41.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 44.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 44.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-248}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+245}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+91}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -3.5e+110)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -1.5e+71)
     (* x (* y0 (- (* c y2) (* b j))))
     (if (<= b -7.5e-84)
       (- 0.0 (* a (* y3 (* y y5))))
       (if (<= b 2.25e+91)
         (* i (* z (- (* t c) (* k y1))))
         (* b (* y4 (- (* t j) (* y 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 (b <= -3.5e+110) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.5e+71) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -7.5e-84) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 2.25e+91) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= (-3.5d+110)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-1.5d+71)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-7.5d-84)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 2.25d+91) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = b * (y4 * ((t * j) - (y * 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 (b <= -3.5e+110) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1.5e+71) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -7.5e-84) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 2.25e+91) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = b * (y4 * ((t * j) - (y * 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 b <= -3.5e+110:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -1.5e+71:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -7.5e-84:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 2.25e+91:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = b * (y4 * ((t * j) - (y * 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 (b <= -3.5e+110)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1.5e+71)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -7.5e-84)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 2.25e+91)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * 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 (b <= -3.5e+110)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -1.5e+71)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -7.5e-84)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 2.25e+91)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = b * (y4 * ((t * j) - (y * 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[b, -3.5e+110], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e+71], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e-84], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+91], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.4999999999999999e110

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 61.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 61.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -3.4999999999999999e110 < b < -1.50000000000000006e71

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(b \cdot j\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{b} \cdot j\right)\right)\right)\right) \]

      5. *-lowering-*.f64 65.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(b, \color{blue}{j}\right)\right)\right)\right) \]

   8. Simplified 65.6%

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]

   if -1.50000000000000006e71 < b < -7.50000000000000026e-84

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 48.4%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 31.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 44.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 44.8%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -7.50000000000000026e-84 < b < 2.25e91

   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 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 31.1%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 31.5%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 2.25e91 < b

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 64.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 48.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 48.5%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+91}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.26 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.25e+118)
   (* b (* y4 (- (* t j) (* y k))))
   (if (<= y4 -1.26e-29)
     (* b (* a (- (* x y) (* z t))))
     (if (<= y4 7.5e-294)
       (* a (* y3 (- (* z y1) (* y y5))))
       (if (<= y4 5.2e+92)
         (* i (* z (- (* t c) (* k y1))))
         (* t (* y4 (- (* b j) (* c y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.25e+118) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.26e-29) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= 7.5e-294) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 5.2e+92) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.25d+118)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y4 <= (-1.26d-29)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y4 <= 7.5d-294) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y4 <= 5.2d+92) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = t * (y4 * ((b * j) - (c * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.25e+118) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y4 <= -1.26e-29) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= 7.5e-294) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 5.2e+92) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.25e+118:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y4 <= -1.26e-29:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y4 <= 7.5e-294:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y4 <= 5.2e+92:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.25e+118)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y4 <= -1.26e-29)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 7.5e-294)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y4 <= 5.2e+92)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.25e+118)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y4 <= -1.26e-29)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y4 <= 7.5e-294)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y4 <= 5.2e+92)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = t * (y4 * ((b * j) - (c * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.25e+118], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.26e-29], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e-294], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.2e+92], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.24999999999999993e118

   1. Initial program 6.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 53.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -1.24999999999999993e118 < y4 < -1.25999999999999996e-29

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 45.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 45.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.25999999999999996e-29 < y4 < 7.5000000000000004e-294

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 45.3%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 7.5000000000000004e-294 < y4 < 5.1999999999999998e92

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 37.2%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right)\right) \]

   8. Simplified 36.4%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if 5.1999999999999998e92 < y4

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 58.7%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{\left(b \cdot j - c \cdot y2\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(b \cdot j\right), \color{blue}{\left(c \cdot y2\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, j\right), \left(\color{blue}{c} \cdot y2\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, j\right), \mathsf{*.f64}\left(c, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -1.26 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{+92}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (- (* t j) (* y k))))))
   (if (<= y4 -3e+115)
     t_1
     (if (<= y4 -2.2e-30)
       (* b (* a (- (* x y) (* z t))))
       (if (<= y4 1.2e-293)
         (* a (* y3 (- (* z y1) (* y y5))))
         (if (<= y4 4e+177) (* i (* z (- (* t c) (* k y1)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y4 <= -3e+115) {
		tmp = t_1;
	} else if (y4 <= -2.2e-30) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= 1.2e-293) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 4e+177) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * ((t * j) - (y * k)))
    if (y4 <= (-3d+115)) then
        tmp = t_1
    else if (y4 <= (-2.2d-30)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y4 <= 1.2d-293) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y4 <= 4d+177) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * ((t * j) - (y * k)));
	double tmp;
	if (y4 <= -3e+115) {
		tmp = t_1;
	} else if (y4 <= -2.2e-30) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y4 <= 1.2e-293) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y4 <= 4e+177) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * ((t * j) - (y * k)))
	tmp = 0
	if y4 <= -3e+115:
		tmp = t_1
	elif y4 <= -2.2e-30:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y4 <= 1.2e-293:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y4 <= 4e+177:
		tmp = i * (z * ((t * c) - (k * y1)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))))
	tmp = 0.0
	if (y4 <= -3e+115)
		tmp = t_1;
	elseif (y4 <= -2.2e-30)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y4 <= 1.2e-293)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y4 <= 4e+177)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * ((t * j) - (y * k)));
	tmp = 0.0;
	if (y4 <= -3e+115)
		tmp = t_1;
	elseif (y4 <= -2.2e-30)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y4 <= 1.2e-293)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y4 <= 4e+177)
		tmp = i * (z * ((t * c) - (k * y1)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3e+115], t$95$1, If[LessEqual[y4, -2.2e-30], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.2e-293], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4e+177], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -3e115 or 4e177 < y4

   1. Initial program 11.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 53.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 53.1%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3e115 < y4 < -2.19999999999999983e-30

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 45.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 45.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.19999999999999983e-30 < y4 < 1.2e-293

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 45.3%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 1.2e-293 < y4 < 4e177

   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 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 39.4%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in z 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot t\right), \color{blue}{\left(k \cdot y1\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 33.8%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, t\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right)\right)\right) \]

   8. Simplified 33.8%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.2 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-61}:\\ \;\;\;\;0 - y0 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4.3e+100)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= x -2.75e-61)
     (- 0.0 (* y0 (* k (* y2 y5))))
     (if (<= x 1.02e+30)
       (* b (* y4 (- (* t j) (* y k))))
       (if (<= x 8.5e+212)
         (* b (* x (- (* y a) (* j y0))))
         (* i (* j (* x 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 (x <= -4.3e+100) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (x <= -2.75e-61) {
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	} else if (x <= 1.02e+30) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 8.5e+212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = i * (j * (x * 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 (x <= (-4.3d+100)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (x <= (-2.75d-61)) then
        tmp = 0.0d0 - (y0 * (k * (y2 * y5)))
    else if (x <= 1.02d+30) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (x <= 8.5d+212) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = i * (j * (x * 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 (x <= -4.3e+100) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (x <= -2.75e-61) {
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	} else if (x <= 1.02e+30) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (x <= 8.5e+212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = i * (j * (x * 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 x <= -4.3e+100:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif x <= -2.75e-61:
		tmp = 0.0 - (y0 * (k * (y2 * y5)))
	elif x <= 1.02e+30:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif x <= 8.5e+212:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = i * (j * (x * 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 (x <= -4.3e+100)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (x <= -2.75e-61)
		tmp = Float64(0.0 - Float64(y0 * Float64(k * Float64(y2 * y5))));
	elseif (x <= 1.02e+30)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 8.5e+212)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(i * Float64(j * Float64(x * 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 (x <= -4.3e+100)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (x <= -2.75e-61)
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	elseif (x <= 1.02e+30)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (x <= 8.5e+212)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = i * (j * (x * 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[x, -4.3e+100], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.75e-61], N[(0.0 - N[(y0 * N[(k * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+30], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+212], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.29999999999999993e100

   1. Initial program 15.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 44.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if -4.29999999999999993e100 < x < -2.7499999999999998e-61

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 53.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 38.5%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 38.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(\mathsf{neg}\left(k \cdot \left(y2 \cdot y5\right)\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(k \cdot \color{blue}{\left(\mathsf{neg}\left(y2 \cdot y5\right)\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(k \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(y2 \cdot y5\right)\right)}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \left(\mathsf{neg}\left(y2 \cdot y5\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \left(0 - \color{blue}{y2 \cdot y5}\right)\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 35.6%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 35.6%

       \[\leadsto y0 \cdot \color{blue}{\left(k \cdot \left(0 - y5 \cdot y2\right)\right)} \]

   if -2.7499999999999998e-61 < x < 1.02e30

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 41.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 31.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right)\right) \]

   8. Simplified 31.2%

      \[\leadsto b \cdot \color{blue}{\left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.02e30 < x < 8.49999999999999979e212

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(a \cdot y\right), \color{blue}{\left(j \cdot y0\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{j} \cdot y0\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.6%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{*.f64}\left(j, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 50.6%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 8.49999999999999979e212 < x

   1. Initial program 14.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 33.6%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around 0

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(x \cdot y1\right) \cdot \color{blue}{j}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(x \cdot y1\right), \color{blue}{j}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(y1 \cdot x\right), j\right)\right) \]

       5. *-lowering-*.f64 45.2%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, x\right), j\right)\right) \]

   11. Simplified 45.2%

       \[\leadsto \color{blue}{i \cdot \left(\left(y1 \cdot x\right) \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-61}:\\ \;\;\;\;0 - y0 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 34.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -4.4 \cdot 10^{-215}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+204}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -4.4e-215)
   (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (- (* x y2) (* z y3)))))
   (if (<= k 5.8e+32)
     (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
     (if (<= k 6.6e+204)
       (* (* y1 y2) (- (* k y4) (* x a)))
       (* (* k y0) (- (* 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 (k <= -4.4e-215) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	} else if (k <= 5.8e+32) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 6.6e+204) {
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	} else {
		tmp = (k * y0) * ((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 (k <= (-4.4d-215)) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))))
    else if (k <= 5.8d+32) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (k <= 6.6d+204) then
        tmp = (y1 * y2) * ((k * y4) - (x * a))
    else
        tmp = (k * y0) * ((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 (k <= -4.4e-215) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	} else if (k <= 5.8e+32) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (k <= 6.6e+204) {
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	} else {
		tmp = (k * y0) * ((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 k <= -4.4e-215:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))))
	elif k <= 5.8e+32:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif k <= 6.6e+204:
		tmp = (y1 * y2) * ((k * y4) - (x * a))
	else:
		tmp = (k * y0) * ((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 (k <= -4.4e-215)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (k <= 5.8e+32)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (k <= 6.6e+204)
		tmp = Float64(Float64(y1 * y2) * Float64(Float64(k * y4) - Float64(x * a)));
	else
		tmp = Float64(Float64(k * y0) * 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 (k <= -4.4e-215)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * ((x * y2) - (z * y3))));
	elseif (k <= 5.8e+32)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (k <= 6.6e+204)
		tmp = (y1 * y2) * ((k * y4) - (x * a));
	else
		tmp = (k * y0) * ((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[k, -4.4e-215], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.8e+32], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.6e+204], N[(N[(y1 * y2), $MachinePrecision] * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -4.39999999999999993e-215

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 52.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 46.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -4.39999999999999993e-215 < k < 5.80000000000000006e32

   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 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 37.1%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot x - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in k around 0

      \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \color{blue}{\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{t} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y0 \cdot c\right), \left(a \cdot y1\right)\right)\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \left(a \cdot y1\right)\right)\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \left(y1 \cdot a\right)\right)\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \left(t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \color{blue}{\left(c \cdot y4 - a \cdot y5\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(c \cdot y4\right), \color{blue}{\left(a \cdot y5\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(y4 \cdot c\right), \left(\color{blue}{a} \cdot y5\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y4, c\right), \left(\color{blue}{a} \cdot y5\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y4, c\right), \left(y5 \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 39.2%

          \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, c\right), \mathsf{*.f64}\left(y1, a\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y4, c\right), \mathsf{*.f64}\left(y5, \color{blue}{a}\right)\right)\right)\right)\right) \]

   8. Simplified 39.2%

      \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(y0 \cdot c - y1 \cdot a\right) - t \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   if 5.80000000000000006e32 < k < 6.5999999999999995e204

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 22.6%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot x - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y2\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y2\right), \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(\color{blue}{-1 \cdot \left(a \cdot x\right)} + k \cdot y4\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(k \cdot y4 + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(k \cdot y4 + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \left(k \cdot y4 - \color{blue}{a \cdot x}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{\_.f64}\left(\left(k \cdot y4\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \left(x \cdot \color{blue}{a}\right)\right)\right) \]

      10. *-lowering-*.f64 52.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 52.4%

      \[\leadsto \color{blue}{\left(y1 \cdot y2\right) \cdot \left(k \cdot y4 - x \cdot a\right)} \]

   if 6.5999999999999995e204 < k

   1. Initial program 8.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(k \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(k \cdot y0\right), \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), \mathsf{\_.f64}\left(\left(y2 \cdot y5\right), \left(b \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \left(b \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, y5\right), \mathsf{*.f64}\left(b, z\right)\right)\right)\right) \]

   8. Simplified 68.6%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5 - b \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.4 \cdot 10^{-215}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{+204}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4 - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-238}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(0 - y4 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.4e+72)
   (* y0 (* b (* z k)))
   (if (<= b -1.7e-238)
     (- 0.0 (* a (* y3 (* y y5))))
     (if (<= b 6.6e-115)
       (* c (* x (* y0 y2)))
       (if (<= b 1.25e+80)
         (* c (- 0.0 (* y4 (* t y2))))
         (* b (* z (* k y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.4e+72) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -1.7e-238) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 6.6e-115) {
		tmp = c * (x * (y0 * y2));
	} else if (b <= 1.25e+80) {
		tmp = c * (0.0 - (y4 * (t * y2)));
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.4d+72)) then
        tmp = y0 * (b * (z * k))
    else if (b <= (-1.7d-238)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 6.6d-115) then
        tmp = c * (x * (y0 * y2))
    else if (b <= 1.25d+80) then
        tmp = c * (0.0d0 - (y4 * (t * y2)))
    else
        tmp = b * (z * (k * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.4e+72) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -1.7e-238) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 6.6e-115) {
		tmp = c * (x * (y0 * y2));
	} else if (b <= 1.25e+80) {
		tmp = c * (0.0 - (y4 * (t * y2)));
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.4e+72:
		tmp = y0 * (b * (z * k))
	elif b <= -1.7e-238:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 6.6e-115:
		tmp = c * (x * (y0 * y2))
	elif b <= 1.25e+80:
		tmp = c * (0.0 - (y4 * (t * y2)))
	else:
		tmp = b * (z * (k * y0))
	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 (b <= -1.4e+72)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (b <= -1.7e-238)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 6.6e-115)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (b <= 1.25e+80)
		tmp = Float64(c * Float64(0.0 - Float64(y4 * Float64(t * y2))));
	else
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.4e+72)
		tmp = y0 * (b * (z * k));
	elseif (b <= -1.7e-238)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 6.6e-115)
		tmp = c * (x * (y0 * y2));
	elseif (b <= 1.25e+80)
		tmp = c * (0.0 - (y4 * (t * y2)));
	else
		tmp = b * (z * (k * y0));
	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[b, -1.4e+72], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-238], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e-115], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+80], N[(c * N[(0.0 - N[(y4 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4e72

   1. Initial program 15.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 50.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 55.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 42.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 42.1%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

   if -1.4e72 < b < -1.69999999999999992e-238

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 35.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 35.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 36.0%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 36.0%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -1.69999999999999992e-238 < b < 6.59999999999999979e-115

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 37.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   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 33.7%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 33.7%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y0 \cdot y2\right) \cdot \color{blue}{x}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y0 \cdot y2\right), \color{blue}{x}\right)\right) \]

       4. *-lowering-*.f64 29.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, y2\right), x\right)\right) \]

   11. Simplified 29.9%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   if 6.59999999999999979e-115 < b < 1.2499999999999999e80

   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 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 42.8%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 29.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 29.4%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 25.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   11. Simplified 25.3%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y2 \cdot y4\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y2\right) \cdot y4\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y2\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y2 \cdot t\right), \left(\mathsf{neg}\left(\color{blue}{y4}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, t\right), \left(\mathsf{neg}\left(\color{blue}{y4}\right)\right)\right)\right) \]

       7. neg-lowering-neg.f64 27.2%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, t\right), \mathsf{neg.f64}\left(y4\right)\right)\right) \]

   13. Applied egg-rr 27.2%

       \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-y4\right)\right)} \]

   if 1.2499999999999999e80 < b

   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 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 47.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 39.0%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 39.0%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 26.7%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 26.7%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-238}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(0 - y4 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+85}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(0 - c\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-296}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(0 - y4 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+212}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(0 - y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -9.4e+85)
   (* (* x i) (* y (- 0.0 c)))
   (if (<= x 7.8e-296)
     (* y0 (* b (* z k)))
     (if (<= x 6.8e+79)
       (* c (- 0.0 (* y4 (* t y2))))
       (if (<= x 1.9e+212)
         (* b (* j (* x (- 0.0 y0))))
         (* y0 (* c (* x y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -9.4e+85) {
		tmp = (x * i) * (y * (0.0 - c));
	} else if (x <= 7.8e-296) {
		tmp = y0 * (b * (z * k));
	} else if (x <= 6.8e+79) {
		tmp = c * (0.0 - (y4 * (t * y2)));
	} else if (x <= 1.9e+212) {
		tmp = b * (j * (x * (0.0 - y0)));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-9.4d+85)) then
        tmp = (x * i) * (y * (0.0d0 - c))
    else if (x <= 7.8d-296) then
        tmp = y0 * (b * (z * k))
    else if (x <= 6.8d+79) then
        tmp = c * (0.0d0 - (y4 * (t * y2)))
    else if (x <= 1.9d+212) then
        tmp = b * (j * (x * (0.0d0 - y0)))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -9.4e+85) {
		tmp = (x * i) * (y * (0.0 - c));
	} else if (x <= 7.8e-296) {
		tmp = y0 * (b * (z * k));
	} else if (x <= 6.8e+79) {
		tmp = c * (0.0 - (y4 * (t * y2)));
	} else if (x <= 1.9e+212) {
		tmp = b * (j * (x * (0.0 - y0)));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -9.4e+85:
		tmp = (x * i) * (y * (0.0 - c))
	elif x <= 7.8e-296:
		tmp = y0 * (b * (z * k))
	elif x <= 6.8e+79:
		tmp = c * (0.0 - (y4 * (t * y2)))
	elif x <= 1.9e+212:
		tmp = b * (j * (x * (0.0 - y0)))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -9.4e+85)
		tmp = Float64(Float64(x * i) * Float64(y * Float64(0.0 - c)));
	elseif (x <= 7.8e-296)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (x <= 6.8e+79)
		tmp = Float64(c * Float64(0.0 - Float64(y4 * Float64(t * y2))));
	elseif (x <= 1.9e+212)
		tmp = Float64(b * Float64(j * Float64(x * Float64(0.0 - y0))));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -9.4e+85)
		tmp = (x * i) * (y * (0.0 - c));
	elseif (x <= 7.8e-296)
		tmp = y0 * (b * (z * k));
	elseif (x <= 6.8e+79)
		tmp = c * (0.0 - (y4 * (t * y2)));
	elseif (x <= 1.9e+212)
		tmp = b * (j * (x * (0.0 - y0)));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -9.4e+85], N[(N[(x * i), $MachinePrecision] * N[(y * N[(0.0 - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-296], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+79], N[(c * N[(0.0 - N[(y4 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+212], N[(b * N[(j * N[(x * N[(0.0 - y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.4000000000000004e85

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 25.8%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 57.9%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \color{blue}{\left(c \cdot y\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 43.5%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(c, y\right)\right)\right) \]

   11. Simplified 43.5%

       \[\leadsto -\left(i \cdot x\right) \cdot \color{blue}{\left(c \cdot y\right)} \]

   if -9.4000000000000004e85 < x < 7.80000000000000021e-296

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 47.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 29.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 29.9%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 26.5%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 26.5%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

   if 7.80000000000000021e-296 < x < 6.80000000000000063e79

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 35.1%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 25.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 25.7%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 21.7%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   11. Simplified 21.7%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y2 \cdot y4\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y2\right) \cdot y4\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y2\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y2 \cdot t\right), \left(\mathsf{neg}\left(\color{blue}{y4}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, t\right), \left(\mathsf{neg}\left(\color{blue}{y4}\right)\right)\right)\right) \]

       7. neg-lowering-neg.f64 23.0%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, t\right), \mathsf{neg.f64}\left(y4\right)\right)\right) \]

   13. Applied egg-rr 23.0%

       \[\leadsto c \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-y4\right)\right)} \]

   if 6.80000000000000063e79 < x < 1.89999999999999994e212

   1. Initial program 19.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 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 b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(j \cdot \left(x \cdot y0\right)\right) \cdot b\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \left(j \cdot \left(x \cdot y0\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \]

       4. mul-1-neg N/A

          \[\leadsto \left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-1 \cdot \color{blue}{b}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(j \cdot \left(x \cdot y0\right)\right), \color{blue}{\left(-1 \cdot b\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\left(x \cdot y0\right) \cdot j\right), \left(\color{blue}{-1} \cdot b\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot y0\right), j\right), \left(\color{blue}{-1} \cdot b\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(y0 \cdot x\right), j\right), \left(-1 \cdot b\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, x\right), j\right), \left(-1 \cdot b\right)\right) \]

       10. mul-1-neg N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, x\right), j\right), \left(\mathsf{neg}\left(b\right)\right)\right) \]

       11. neg-lowering-neg.f64 39.3%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, x\right), j\right), \mathsf{neg.f64}\left(b\right)\right) \]

   11. Simplified 39.3%

       \[\leadsto \color{blue}{\left(\left(y0 \cdot x\right) \cdot j\right) \cdot \left(-b\right)} \]

   if 1.89999999999999994e212 < x

   1. Initial program 13.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 32.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   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 49.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 49.1%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \left(y2 \cdot \color{blue}{x}\right)\right)\right) \]

       2. *-lowering-*.f64 46.6%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y2, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 46.6%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+85}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(0 - c\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-296}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(0 - y4 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+212}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(0 - y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-62}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+176}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.55e+71)
   (* y0 (* b (* z k)))
   (if (<= b -2.4e-245)
     (- 0.0 (* a (* y3 (* y y5))))
     (if (<= b 7.6e-62)
       (* k (- 0.0 (* y0 (* y2 y5))))
       (if (<= b 1.3e+176) (* (* k y1) (* y2 y4)) (* b (* z (* k y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.55e+71) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -2.4e-245) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 7.6e-62) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else if (b <= 1.3e+176) {
		tmp = (k * y1) * (y2 * y4);
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.55d+71)) then
        tmp = y0 * (b * (z * k))
    else if (b <= (-2.4d-245)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 7.6d-62) then
        tmp = k * (0.0d0 - (y0 * (y2 * y5)))
    else if (b <= 1.3d+176) then
        tmp = (k * y1) * (y2 * y4)
    else
        tmp = b * (z * (k * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.55e+71) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -2.4e-245) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 7.6e-62) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else if (b <= 1.3e+176) {
		tmp = (k * y1) * (y2 * y4);
	} else {
		tmp = b * (z * (k * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.55e+71:
		tmp = y0 * (b * (z * k))
	elif b <= -2.4e-245:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 7.6e-62:
		tmp = k * (0.0 - (y0 * (y2 * y5)))
	elif b <= 1.3e+176:
		tmp = (k * y1) * (y2 * y4)
	else:
		tmp = b * (z * (k * y0))
	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 (b <= -1.55e+71)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (b <= -2.4e-245)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 7.6e-62)
		tmp = Float64(k * Float64(0.0 - Float64(y0 * Float64(y2 * y5))));
	elseif (b <= 1.3e+176)
		tmp = Float64(Float64(k * y1) * Float64(y2 * y4));
	else
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.55e+71)
		tmp = y0 * (b * (z * k));
	elseif (b <= -2.4e-245)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 7.6e-62)
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	elseif (b <= 1.3e+176)
		tmp = (k * y1) * (y2 * y4);
	else
		tmp = b * (z * (k * y0));
	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[b, -1.55e+71], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-245], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e-62], N[(k * N[(0.0 - N[(y0 * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e+176], N[(N[(k * y1), $MachinePrecision] * N[(y2 * y4), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.55000000000000009e71

   1. Initial program 15.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 50.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 55.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 42.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 42.1%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

   if -1.55000000000000009e71 < b < -2.4e-245

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 34.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 34.7%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -2.4e-245 < b < 7.60000000000000013e-62

   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 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 37.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 35.7%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 35.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto k \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto k \cdot \left(-1 \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(0 - \color{blue}{y0 \cdot \left(y2 \cdot y5\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \left(y5 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 31.5%

           \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y5, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 31.5%

       \[\leadsto \color{blue}{k \cdot \left(0 - y0 \cdot \left(y5 \cdot y2\right)\right)} \]

   if 7.60000000000000013e-62 < b < 1.29999999999999995e176

   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 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 47.1%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 27.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 27.2%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 24.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right) \]

   11. Simplified 24.0%

       \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1\right)} \]

   if 1.29999999999999995e176 < b

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 40.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 34.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 34.1%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 34.6%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 34.6%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-62}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+176}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 700:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2e+113)
   (* y0 (* b (- (* z k) (* x j))))
   (if (<= b -1e-203)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= b 700.0)
       (* y2 (* y1 (- (* k y4) (* x a))))
       (* t (* y4 (- (* b j) (* c y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -2e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1e-203) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 700.0) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-2d+113)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (b <= (-1d-203)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 700.0d0) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else
        tmp = t * (y4 * ((b * j) - (c * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -2e+113) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (b <= -1e-203) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 700.0) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else {
		tmp = t * (y4 * ((b * j) - (c * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -2e+113:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif b <= -1e-203:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 700.0:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	else:
		tmp = t * (y4 * ((b * j) - (c * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -2e+113)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -1e-203)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 700.0)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	else
		tmp = Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -2e+113)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (b <= -1e-203)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 700.0)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	else
		tmp = t * (y4 * ((b * j) - (c * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -2e+113], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-203], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 700.0], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2e113

   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 53.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 63.0%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -2e113 < b < -1e-203

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 38.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 38.3%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(c \cdot z\right) + j \cdot y5\right)}\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \color{blue}{-1 \cdot \left(c \cdot z\right)}\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 + \left(\mathsf{neg}\left(c \cdot z\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \left(j \cdot y5 - \color{blue}{c \cdot z}\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(j \cdot y5\right), \color{blue}{\left(c \cdot z\right)}\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y5 \cdot j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(\color{blue}{c} \cdot z\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \left(z \cdot \color{blue}{c}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 42.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y5, j\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   11. Simplified 42.0%

       \[\leadsto y0 \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot j - z \cdot c\right)\right)} \]

   if -1e-203 < b < 700

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 39.7%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(c \cdot y0 - a \cdot y1\right) \cdot x - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \mathsf{*.f64}\left(y2, \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)}\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \left(k \cdot y4 + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \left(k \cdot y4 + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \left(k \cdot y4 - \color{blue}{a \cdot x}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y4\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \left(\color{blue}{a} \cdot x\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \left(x \cdot \color{blue}{a}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 40.2%

         \[\leadsto \mathsf{*.f64}\left(y2, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y4\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right)\right)\right) \]

   8. Simplified 40.2%

      \[\leadsto y2 \cdot \color{blue}{\left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)} \]

   if 700 < b

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 40.7%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{\left(b \cdot j - c \cdot y2\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(b \cdot j\right), \color{blue}{\left(c \cdot y2\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, j\right), \left(\color{blue}{c} \cdot y2\right)\right)\right)\right) \]

      5. *-lowering-*.f64 42.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, j\right), \mathsf{*.f64}\left(c, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 42.2%

      \[\leadsto \color{blue}{t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+113}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 700:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 24.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-244}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2.6e+70)
   (* y0 (* b (* z k)))
   (if (<= b -1.7e-244)
     (- 0.0 (* a (* y3 (* y y5))))
     (if (<= b 1.8e-52)
       (* k (- 0.0 (* y0 (* y2 y5))))
       (* b (* a (- (* x y) (* z t))))))))

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 (b <= -2.6e+70) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -1.7e-244) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 1.8e-52) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else {
		tmp = b * (a * ((x * y) - (z * t)));
	}
	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 (b <= (-2.6d+70)) then
        tmp = y0 * (b * (z * k))
    else if (b <= (-1.7d-244)) then
        tmp = 0.0d0 - (a * (y3 * (y * y5)))
    else if (b <= 1.8d-52) then
        tmp = k * (0.0d0 - (y0 * (y2 * y5)))
    else
        tmp = b * (a * ((x * y) - (z * t)))
    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 (b <= -2.6e+70) {
		tmp = y0 * (b * (z * k));
	} else if (b <= -1.7e-244) {
		tmp = 0.0 - (a * (y3 * (y * y5)));
	} else if (b <= 1.8e-52) {
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	} else {
		tmp = b * (a * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -2.6e+70:
		tmp = y0 * (b * (z * k))
	elif b <= -1.7e-244:
		tmp = 0.0 - (a * (y3 * (y * y5)))
	elif b <= 1.8e-52:
		tmp = k * (0.0 - (y0 * (y2 * y5)))
	else:
		tmp = b * (a * ((x * y) - (z * t)))
	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 (b <= -2.6e+70)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (b <= -1.7e-244)
		tmp = Float64(0.0 - Float64(a * Float64(y3 * Float64(y * y5))));
	elseif (b <= 1.8e-52)
		tmp = Float64(k * Float64(0.0 - Float64(y0 * Float64(y2 * y5))));
	else
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	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 (b <= -2.6e+70)
		tmp = y0 * (b * (z * k));
	elseif (b <= -1.7e-244)
		tmp = 0.0 - (a * (y3 * (y * y5)));
	elseif (b <= 1.8e-52)
		tmp = k * (0.0 - (y0 * (y2 * y5)));
	else
		tmp = b * (a * ((x * y) - (z * t)));
	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[b, -2.6e+70], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-244], N[(0.0 - N[(a * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-52], N[(k * N[(0.0 - N[(y0 * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.6e70

   1. Initial program 15.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 50.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 55.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 55.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 42.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 42.1%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

   if -2.6e70 < b < -1.70000000000000004e-244

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(0 - \color{blue}{y \cdot y5}\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 34.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y}\right)\right)\right)\right) \]

   11. Simplified 34.7%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(0 - y5 \cdot y\right)}\right) \]

   if -1.70000000000000004e-244 < b < 1.79999999999999994e-52

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 36.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 35.1%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto k \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto k \cdot \left(-1 \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(\mathsf{neg}\left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(0 - \color{blue}{y0 \cdot \left(y2 \cdot y5\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \left(y5 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       10. *-lowering-*.f64 31.0%

           \[\leadsto \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y5, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 31.0%

       \[\leadsto \color{blue}{k \cdot \left(0 - y0 \cdot \left(y5 \cdot y2\right)\right)} \]

   if 1.79999999999999994e-52 < b

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 33.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 33.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-244}:\\ \;\;\;\;0 - a \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;k \cdot \left(0 - y0 \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 26.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.2 \cdot 10^{+179}:\\ \;\;\;\;0 - y0 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -1.2e+179)
   (- 0.0 (* y0 (* k (* y2 y5))))
   (if (<= k 7e-54)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= k 1.05e+217) (* (* k y1) (* y2 y4)) (* y0 (* b (* 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 (k <= -1.2e+179) {
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	} else if (k <= 7e-54) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (k <= 1.05e+217) {
		tmp = (k * y1) * (y2 * y4);
	} else {
		tmp = y0 * (b * (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 (k <= (-1.2d+179)) then
        tmp = 0.0d0 - (y0 * (k * (y2 * y5)))
    else if (k <= 7d-54) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (k <= 1.05d+217) then
        tmp = (k * y1) * (y2 * y4)
    else
        tmp = y0 * (b * (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 (k <= -1.2e+179) {
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	} else if (k <= 7e-54) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (k <= 1.05e+217) {
		tmp = (k * y1) * (y2 * y4);
	} else {
		tmp = y0 * (b * (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 k <= -1.2e+179:
		tmp = 0.0 - (y0 * (k * (y2 * y5)))
	elif k <= 7e-54:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif k <= 1.05e+217:
		tmp = (k * y1) * (y2 * y4)
	else:
		tmp = y0 * (b * (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 (k <= -1.2e+179)
		tmp = Float64(0.0 - Float64(y0 * Float64(k * Float64(y2 * y5))));
	elseif (k <= 7e-54)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (k <= 1.05e+217)
		tmp = Float64(Float64(k * y1) * Float64(y2 * y4));
	else
		tmp = Float64(y0 * Float64(b * 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 (k <= -1.2e+179)
		tmp = 0.0 - (y0 * (k * (y2 * y5)));
	elseif (k <= 7e-54)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (k <= 1.05e+217)
		tmp = (k * y1) * (y2 * y4);
	else
		tmp = y0 * (b * (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[k, -1.2e+179], N[(0.0 - N[(y0 * N[(k * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7e-54], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e+217], N[(N[(k * y1), $MachinePrecision] * N[(y2 * y4), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.20000000000000006e179

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 72.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y5\right)\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 72.5%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y5\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(j, y3\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 72.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(\mathsf{neg}\left(k \cdot \left(y2 \cdot y5\right)\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(k \cdot \color{blue}{\left(\mathsf{neg}\left(y2 \cdot y5\right)\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(k \cdot \left(-1 \cdot \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \color{blue}{\left(-1 \cdot \left(y2 \cdot y5\right)\right)}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \left(\mathsf{neg}\left(y2 \cdot y5\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \left(0 - \color{blue}{y2 \cdot y5}\right)\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \color{blue}{\left(y2 \cdot y5\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \left(y5 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 61.6%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(k, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y5, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 61.6%

       \[\leadsto y0 \cdot \color{blue}{\left(k \cdot \left(0 - y5 \cdot y2\right)\right)} \]

   if -1.20000000000000006e179 < k < 6.99999999999999964e-54

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 26.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 26.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   if 6.99999999999999964e-54 < k < 1.05e217

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 47.3%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 36.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 36.5%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 38.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right) \]

   11. Simplified 38.8%

       \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1\right)} \]

   if 1.05e217 < k

   1. Initial program 8.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 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 b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 52.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 52.7%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.2 \cdot 10^{+179}:\\ \;\;\;\;0 - y0 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 20.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(0 - c\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-188}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.25e+84)
   (* (* x i) (* y (- 0.0 c)))
   (if (<= x -8e-188)
     (* y0 (* b (* z k)))
     (if (<= x 2.05e-116) (* z (* a (* y1 y3))) (* y0 (* c (* x y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.25e+84) {
		tmp = (x * i) * (y * (0.0 - c));
	} else if (x <= -8e-188) {
		tmp = y0 * (b * (z * k));
	} else if (x <= 2.05e-116) {
		tmp = z * (a * (y1 * y3));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.25d+84)) then
        tmp = (x * i) * (y * (0.0d0 - c))
    else if (x <= (-8d-188)) then
        tmp = y0 * (b * (z * k))
    else if (x <= 2.05d-116) then
        tmp = z * (a * (y1 * y3))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.25e+84) {
		tmp = (x * i) * (y * (0.0 - c));
	} else if (x <= -8e-188) {
		tmp = y0 * (b * (z * k));
	} else if (x <= 2.05e-116) {
		tmp = z * (a * (y1 * y3));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.25e+84:
		tmp = (x * i) * (y * (0.0 - c))
	elif x <= -8e-188:
		tmp = y0 * (b * (z * k))
	elif x <= 2.05e-116:
		tmp = z * (a * (y1 * y3))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.25e+84)
		tmp = Float64(Float64(x * i) * Float64(y * Float64(0.0 - c)));
	elseif (x <= -8e-188)
		tmp = Float64(y0 * Float64(b * Float64(z * k)));
	elseif (x <= 2.05e-116)
		tmp = Float64(z * Float64(a * Float64(y1 * y3)));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.25e+84)
		tmp = (x * i) * (y * (0.0 - c));
	elseif (x <= -8e-188)
		tmp = y0 * (b * (z * k));
	elseif (x <= 2.05e-116)
		tmp = z * (a * (y1 * y3));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.25e+84], N[(N[(x * i), $MachinePrecision] * N[(y * N[(0.0 - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-188], N[(y0 * N[(b * N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-116], N[(z * N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.25e84

   1. Initial program 17.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 25.8%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 57.9%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \color{blue}{\left(c \cdot y\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 43.5%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(c, y\right)\right)\right) \]

   11. Simplified 43.5%

       \[\leadsto -\left(i \cdot x\right) \cdot \color{blue}{\left(c \cdot y\right)} \]

   if -1.25e84 < x < -7.9999999999999996e-188

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 48.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z\right)}\right)\right) \]

       2. *-lowering-*.f64 29.4%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 29.4%

       \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z\right)\right)} \]

   if -7.9999999999999996e-188 < x < 2.0499999999999999e-116

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 28.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 28.8%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 18.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 18.3%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \left(\left(y1 \cdot y3\right) \cdot \color{blue}{z}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(y1 \cdot y3\right)\right) \cdot \color{blue}{z} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(y1 \cdot y3\right)\right), \color{blue}{z}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(y1 \cdot y3\right)\right), z\right) \]

       5. *-lowering-*.f64 25.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, y3\right)\right), z\right) \]

   13. Applied egg-rr 25.5%

       \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]

   if 2.0499999999999999e-116 < x

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 35.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in 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 34.2%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 34.2%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \left(y2 \cdot \color{blue}{x}\right)\right)\right) \]

       2. *-lowering-*.f64 29.3%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y2, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 29.3%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(0 - c\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-188}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 20.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -8.6 \cdot 10^{+61}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{elif}\;y1 \leq 6.1 \cdot 10^{-121}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(c \cdot \left(0 - i\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -8.6e+61)
   (* (* k y1) (* y2 y4))
   (if (<= y1 6.1e-121)
     (* (* x y) (* c (- 0.0 i)))
     (if (<= y1 2.3e+19) (* y0 (* y2 (* x c))) (* z (* a (* y1 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 (y1 <= -8.6e+61) {
		tmp = (k * y1) * (y2 * y4);
	} else if (y1 <= 6.1e-121) {
		tmp = (x * y) * (c * (0.0 - i));
	} else if (y1 <= 2.3e+19) {
		tmp = y0 * (y2 * (x * c));
	} else {
		tmp = z * (a * (y1 * 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 (y1 <= (-8.6d+61)) then
        tmp = (k * y1) * (y2 * y4)
    else if (y1 <= 6.1d-121) then
        tmp = (x * y) * (c * (0.0d0 - i))
    else if (y1 <= 2.3d+19) then
        tmp = y0 * (y2 * (x * c))
    else
        tmp = z * (a * (y1 * 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 (y1 <= -8.6e+61) {
		tmp = (k * y1) * (y2 * y4);
	} else if (y1 <= 6.1e-121) {
		tmp = (x * y) * (c * (0.0 - i));
	} else if (y1 <= 2.3e+19) {
		tmp = y0 * (y2 * (x * c));
	} else {
		tmp = z * (a * (y1 * 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 y1 <= -8.6e+61:
		tmp = (k * y1) * (y2 * y4)
	elif y1 <= 6.1e-121:
		tmp = (x * y) * (c * (0.0 - i))
	elif y1 <= 2.3e+19:
		tmp = y0 * (y2 * (x * c))
	else:
		tmp = z * (a * (y1 * 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 (y1 <= -8.6e+61)
		tmp = Float64(Float64(k * y1) * Float64(y2 * y4));
	elseif (y1 <= 6.1e-121)
		tmp = Float64(Float64(x * y) * Float64(c * Float64(0.0 - i)));
	elseif (y1 <= 2.3e+19)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	else
		tmp = Float64(z * Float64(a * Float64(y1 * 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 (y1 <= -8.6e+61)
		tmp = (k * y1) * (y2 * y4);
	elseif (y1 <= 6.1e-121)
		tmp = (x * y) * (c * (0.0 - i));
	elseif (y1 <= 2.3e+19)
		tmp = y0 * (y2 * (x * c));
	else
		tmp = z * (a * (y1 * 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[y1, -8.6e+61], N[(N[(k * y1), $MachinePrecision] * N[(y2 * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.1e-121], N[(N[(x * y), $MachinePrecision] * N[(c * N[(0.0 - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.3e+19], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -8.6000000000000003e61

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 35.2%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 35.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 35.4%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \color{blue}{\left(k \cdot y1\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 39.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{*.f64}\left(k, \color{blue}{y1}\right)\right) \]

   11. Simplified 39.0%

       \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1\right)} \]

   if -8.6000000000000003e61 < y1 < 6.09999999999999978e-121

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 29.6%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 25.0%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 25.0%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(c \cdot i\right) \cdot \left(x \cdot y\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(c \cdot i\right), \left(x \cdot y\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(c, i\right), \left(x \cdot y\right)\right)\right) \]

       4. *-lowering-*.f64 25.8%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(c, i\right), \mathsf{*.f64}\left(x, y\right)\right)\right) \]

   11. Simplified 25.8%

       \[\leadsto -\color{blue}{\left(c \cdot i\right) \cdot \left(x \cdot y\right)} \]

   if 6.09999999999999978e-121 < y1 < 2.3e19

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 45.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in 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 24.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 24.1%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)}\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \left(\left(c \cdot x\right) \cdot \color{blue}{y2}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\left(c \cdot x\right), \color{blue}{y2}\right)\right) \]

       3. *-lowering-*.f64 27.4%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, x\right), y2\right)\right) \]

   11. Simplified 27.4%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

   if 2.3e19 < y1

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 31.0%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 33.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 33.0%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 24.5%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 24.5%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \left(\left(y1 \cdot y3\right) \cdot \color{blue}{z}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(y1 \cdot y3\right)\right) \cdot \color{blue}{z} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(y1 \cdot y3\right)\right), \color{blue}{z}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(y1 \cdot y3\right)\right), z\right) \]

       5. *-lowering-*.f64 31.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, y3\right)\right), z\right) \]

   13. Applied egg-rr 31.3%

       \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -8.6 \cdot 10^{+61}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4\right)\\ \mathbf{elif}\;y1 \leq 6.1 \cdot 10^{-121}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(c \cdot \left(0 - i\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 21.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 10^{-44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4.4e+105)
   (* i (* j (* x y1)))
   (if (<= x -2.4e-33)
     (* k (* y4 (* y1 y2)))
     (if (<= x 1e-44) (* b (* z (* k y0))) (* y0 (* c (* x y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.4e+105) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.4e-33) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 1e-44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-4.4d+105)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-2.4d-33)) then
        tmp = k * (y4 * (y1 * y2))
    else if (x <= 1d-44) then
        tmp = b * (z * (k * y0))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.4e+105) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.4e-33) {
		tmp = k * (y4 * (y1 * y2));
	} else if (x <= 1e-44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -4.4e+105:
		tmp = i * (j * (x * y1))
	elif x <= -2.4e-33:
		tmp = k * (y4 * (y1 * y2))
	elif x <= 1e-44:
		tmp = b * (z * (k * y0))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -4.4e+105)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -2.4e-33)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (x <= 1e-44)
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -4.4e+105)
		tmp = i * (j * (x * y1));
	elseif (x <= -2.4e-33)
		tmp = k * (y4 * (y1 * y2));
	elseif (x <= 1e-44)
		tmp = b * (z * (k * y0));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -4.4e+105], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-33], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-44], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.40000000000000014e105

   1. Initial program 10.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 24.2%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 62.8%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around 0

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(x \cdot y1\right) \cdot \color{blue}{j}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(x \cdot y1\right), \color{blue}{j}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(y1 \cdot x\right), j\right)\right) \]

       5. *-lowering-*.f64 42.3%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, x\right), j\right)\right) \]

   11. Simplified 42.3%

       \[\leadsto \color{blue}{i \cdot \left(\left(y1 \cdot x\right) \cdot j\right)} \]

   if -4.40000000000000014e105 < x < -2.4e-33

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 41.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k 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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(\left(y1 \cdot y2\right) \cdot \color{blue}{y4}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(\left(y1 \cdot y2\right), \color{blue}{y4}\right)\right) \]

       4. *-lowering-*.f64 38.3%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), y4\right)\right) \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{k \cdot \left(\left(y1 \cdot y2\right) \cdot y4\right)} \]

   if -2.4e-33 < x < 9.99999999999999953e-45

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 46.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 25.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 25.3%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 21.9%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 21.9%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if 9.99999999999999953e-45 < x

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 35.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   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 36.5%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 36.5%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot y2\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \left(y2 \cdot \color{blue}{x}\right)\right)\right) \]

       2. *-lowering-*.f64 33.0%

          \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y2, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 33.0%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 10^{-44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -2.3 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* z (* k y0)))))
   (if (<= y0 -2.3e+64) t_1 (if (<= y0 4.4e-64) (* k (* y4 (* y1 y2))) 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 * (z * (k * y0));
	double tmp;
	if (y0 <= -2.3e+64) {
		tmp = t_1;
	} else if (y0 <= 4.4e-64) {
		tmp = k * (y4 * (y1 * y2));
	} 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 * (z * (k * y0))
    if (y0 <= (-2.3d+64)) then
        tmp = t_1
    else if (y0 <= 4.4d-64) then
        tmp = k * (y4 * (y1 * y2))
    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 * (z * (k * y0));
	double tmp;
	if (y0 <= -2.3e+64) {
		tmp = t_1;
	} else if (y0 <= 4.4e-64) {
		tmp = k * (y4 * (y1 * y2));
	} 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 * (z * (k * y0))
	tmp = 0
	if y0 <= -2.3e+64:
		tmp = t_1
	elif y0 <= 4.4e-64:
		tmp = k * (y4 * (y1 * y2))
	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(z * Float64(k * y0)))
	tmp = 0.0
	if (y0 <= -2.3e+64)
		tmp = t_1;
	elseif (y0 <= 4.4e-64)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	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 * (z * (k * y0));
	tmp = 0.0;
	if (y0 <= -2.3e+64)
		tmp = t_1;
	elseif (y0 <= 4.4e-64)
		tmp = k * (y4 * (y1 * y2));
	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[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.3e+64], t$95$1, If[LessEqual[y0, 4.4e-64], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y0 < -2.3e64 or 4.3999999999999999e-64 < y0

   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 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 50.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.6%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 40.6%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 31.5%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 31.5%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if -2.3e64 < y0 < 4.3999999999999999e-64

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 40.0%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 30.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 30.2%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k 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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(k, \left(\left(y1 \cdot y2\right) \cdot \color{blue}{y4}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(\left(y1 \cdot y2\right), \color{blue}{y4}\right)\right) \]

       4. *-lowering-*.f64 22.9%

          \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y2\right), y4\right)\right) \]

   11. Simplified 22.9%

       \[\leadsto \color{blue}{k \cdot \left(\left(y1 \cdot y2\right) \cdot y4\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.3 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* j (* x y1)))))
   (if (<= x -2.2e+100) t_1 (if (<= x 1.9e+44) (* b (* z (* k y0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (x <= -2.2e+100) {
		tmp = t_1;
	} else if (x <= 1.9e+44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (j * (x * y1))
    if (x <= (-2.2d+100)) then
        tmp = t_1
    else if (x <= 1.9d+44) then
        tmp = b * (z * (k * y0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (j * (x * y1));
	double tmp;
	if (x <= -2.2e+100) {
		tmp = t_1;
	} else if (x <= 1.9e+44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (j * (x * y1))
	tmp = 0
	if x <= -2.2e+100:
		tmp = t_1
	elif x <= 1.9e+44:
		tmp = b * (z * (k * y0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(j * Float64(x * y1)))
	tmp = 0.0
	if (x <= -2.2e+100)
		tmp = t_1;
	elseif (x <= 1.9e+44)
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (j * (x * y1));
	tmp = 0.0;
	if (x <= -2.2e+100)
		tmp = t_1;
	elseif (x <= 1.9e+44)
		tmp = b * (z * (k * y0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+100], t$95$1, If[LessEqual[x, 1.9e+44], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e100 or 1.9000000000000001e44 < x

   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 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 28.5%

      \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(y5 \cdot \left(t \cdot j - k \cdot y\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(c \cdot y - j \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\left(c \cdot y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \left(j \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 49.7%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y\right), \mathsf{*.f64}\left(j, y1\right)\right)\right)\right) \]

   8. Simplified 49.7%

      \[\leadsto \color{blue}{-\left(i \cdot x\right) \cdot \left(c \cdot y - j \cdot y1\right)} \]

   9. Taylor expanded in c around 0

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot \left(x \cdot y1\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(x \cdot y1\right) \cdot \color{blue}{j}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(x \cdot y1\right), \color{blue}{j}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(y1 \cdot x\right), j\right)\right) \]

       5. *-lowering-*.f64 34.0%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, x\right), j\right)\right) \]

   11. Simplified 34.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(y1 \cdot x\right) \cdot j\right)} \]

   if -2.2000000000000001e100 < x < 1.9000000000000001e44

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 47.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 25.9%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 25.9%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 21.5%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 18.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4.6e+159)
   (* a (* y1 (* z y3)))
   (if (<= x 2.7e-44) (* b (* z (* k y0))) (* c (* x (* y0 y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.6e+159) {
		tmp = a * (y1 * (z * y3));
	} else if (x <= 2.7e-44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-4.6d+159)) then
        tmp = a * (y1 * (z * y3))
    else if (x <= 2.7d-44) then
        tmp = b * (z * (k * y0))
    else
        tmp = c * (x * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.6e+159) {
		tmp = a * (y1 * (z * y3));
	} else if (x <= 2.7e-44) {
		tmp = b * (z * (k * y0));
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -4.6e+159:
		tmp = a * (y1 * (z * y3))
	elif x <= 2.7e-44:
		tmp = b * (z * (k * y0))
	else:
		tmp = c * (x * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -4.6e+159)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (x <= 2.7e-44)
		tmp = Float64(b * Float64(z * Float64(k * y0)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -4.6e+159)
		tmp = a * (y1 * (z * y3));
	elseif (x <= 2.7e-44)
		tmp = b * (z * (k * y0));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -4.6e+159], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-44], N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999991e159

   1. Initial program 13.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 52.9%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 36.2%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 36.2%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -4.59999999999999991e159 < x < 2.6999999999999999e-44

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 45.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 26.1%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 26.1%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 22.1%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 22.1%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if 2.6999999999999999e-44 < x

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 35.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   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 36.5%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 36.5%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y0 \cdot y2\right) \cdot \color{blue}{x}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y0 \cdot y2\right), \color{blue}{x}\right)\right) \]

       4. *-lowering-*.f64 27.2%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, y2\right), x\right)\right) \]

   11. Simplified 27.2%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 22.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{if}\;y0 \leq -1.8 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* z (* k y0)))))
   (if (<= y0 -1.8e+101) t_1 (if (<= y0 2.1e+16) (* a (* y1 (* z y3))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * (k * y0));
	double tmp;
	if (y0 <= -1.8e+101) {
		tmp = t_1;
	} else if (y0 <= 2.1e+16) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * (k * y0))
    if (y0 <= (-1.8d+101)) then
        tmp = t_1
    else if (y0 <= 2.1d+16) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (z * (k * y0));
	double tmp;
	if (y0 <= -1.8e+101) {
		tmp = t_1;
	} else if (y0 <= 2.1e+16) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (z * (k * y0))
	tmp = 0
	if y0 <= -1.8e+101:
		tmp = t_1
	elif y0 <= 2.1e+16:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(z * Float64(k * y0)))
	tmp = 0.0
	if (y0 <= -1.8e+101)
		tmp = t_1;
	elseif (y0 <= 2.1e+16)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (z * (k * y0));
	tmp = 0.0;
	if (y0 <= -1.8e+101)
		tmp = t_1;
	elseif (y0 <= 2.1e+16)
		tmp = a * (y1 * (z * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(z * N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.8e+101], t$95$1, If[LessEqual[y0, 2.1e+16], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y0 < -1.80000000000000015e101 or 2.1e16 < y0

   1. Initial program 17.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 52.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(y0, \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot z - j \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(k \cdot z\right), \color{blue}{\left(j \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{j} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 41.3%

         \[\leadsto \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{*.f64}\left(j, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 41.3%

      \[\leadsto y0 \cdot \color{blue}{\left(b \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(k \cdot y0\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(k \cdot y0\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 34.2%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, y0\right), z\right)\right) \]

   11. Simplified 34.2%

       \[\leadsto \color{blue}{b \cdot \left(\left(k \cdot y0\right) \cdot z\right)} \]

   if -1.80000000000000015e101 < y0 < 2.1e16

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 26.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 26.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 15.6%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 15.6%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.8 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z 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) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   6. associate-*r* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

5. Simplified 35.4%

   \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y3 around -inf

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right)\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right)\right) \]

   5. *-lowering-*.f64 23.2%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right)\right) \]

8. Simplified 23.2%

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]

9. Taylor expanded in y1 around inf

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)}\right) \]

    2. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \color{blue}{\left(y3 \cdot z\right)}\right)\right) \]

    3. *-lowering-*.f64 13.4%

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

11. Simplified 13.4%

    \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

12. Final simplification 13.4%

    \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
13. Add Preprocessing

Developer Target 1: 27.9% 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 2024138 
(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)))))