Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.2% → 43.0%

Time: 32.7s

Alternatives: 32

Speedup: 3.6×

• 88.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.2% 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: 43.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ t_2 := x \cdot j - z \cdot k\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot t\_2 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot \left(\frac{y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)}{t} + \left(b \cdot y4 + \left(\frac{x \cdot \left(i \cdot y1 - b \cdot y0\right)}{t} - i \cdot y5\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot t\_2\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (* y3 (- (* c y4) (* a y5)))
           (+ (* x (- (* a b) (* c i))) (* k (- (* i y5) (* b y4)))))))
        (t_2 (- (* x j) (* z k))))
   (if (<= y -1.15e+78)
     t_1
     (if (<= y -3.6e-11)
       (*
        i
        (+
         (* c (- (* z t) (* x y)))
         (+ (* y1 t_2) (* y5 (- (* y k) (* t j))))))
       (if (<= y -9.5e-284)
         (*
          j
          (*
           t
           (+
            (/ (* y3 (- (* y0 y5) (* y1 y4))) t)
            (+ (* b y4) (- (/ (* x (- (* i y1) (* b y0))) t) (* i y5))))))
         (if (<= y 7e-105)
           (*
            y0
            (+
             (* y5 (- (* j y3) (* k y2)))
             (- (* c (- (* x y2) (* z y3))) (* b t_2))))
           (if (<= y 5e+162)
             (*
              z
              (+
               (* k (- (* b y0) (* i y1)))
               (+ (* y3 (- (* a y1) (* c y0))) (* t (- (* c i) (* a b))))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))));
	double t_2 = (x * j) - (z * k);
	double tmp;
	if (y <= -1.15e+78) {
		tmp = t_1;
	} else if (y <= -3.6e-11) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= -9.5e-284) {
		tmp = j * (t * (((y3 * ((y0 * y5) - (y1 * y4))) / t) + ((b * y4) + (((x * ((i * y1) - (b * y0))) / t) - (i * y5)))));
	} else if (y <= 7e-105) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_2)));
	} else if (y <= 5e+162) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))))
    t_2 = (x * j) - (z * k)
    if (y <= (-1.15d+78)) then
        tmp = t_1
    else if (y <= (-3.6d-11)) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))))
    else if (y <= (-9.5d-284)) then
        tmp = j * (t * (((y3 * ((y0 * y5) - (y1 * y4))) / t) + ((b * y4) + (((x * ((i * y1) - (b * y0))) / t) - (i * y5)))))
    else if (y <= 7d-105) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_2)))
    else if (y <= 5d+162) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))));
	double t_2 = (x * j) - (z * k);
	double tmp;
	if (y <= -1.15e+78) {
		tmp = t_1;
	} else if (y <= -3.6e-11) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= -9.5e-284) {
		tmp = j * (t * (((y3 * ((y0 * y5) - (y1 * y4))) / t) + ((b * y4) + (((x * ((i * y1) - (b * y0))) / t) - (i * y5)))));
	} else if (y <= 7e-105) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_2)));
	} else if (y <= 5e+162) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))))
	t_2 = (x * j) - (z * k)
	tmp = 0
	if y <= -1.15e+78:
		tmp = t_1
	elif y <= -3.6e-11:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))))
	elif y <= -9.5e-284:
		tmp = j * (t * (((y3 * ((y0 * y5) - (y1 * y4))) / t) + ((b * y4) + (((x * ((i * y1) - (b * y0))) / t) - (i * y5)))))
	elif y <= 7e-105:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_2)))
	elif y <= 5e+162:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(k * Float64(Float64(i * y5) - Float64(b * y4))))))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (y <= -1.15e+78)
		tmp = t_1;
	elseif (y <= -3.6e-11)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * t_2) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y <= -9.5e-284)
		tmp = Float64(j * Float64(t * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) / t) + Float64(Float64(b * y4) + Float64(Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) / t) - Float64(i * y5))))));
	elseif (y <= 7e-105)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(b * t_2))));
	elseif (y <= 5e+162)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	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 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))));
	t_2 = (x * j) - (z * k);
	tmp = 0.0;
	if (y <= -1.15e+78)
		tmp = t_1;
	elseif (y <= -3.6e-11)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	elseif (y <= -9.5e-284)
		tmp = j * (t * (((y3 * ((y0 * y5) - (y1 * y4))) / t) + ((b * y4) + (((x * ((i * y1) - (b * y0))) / t) - (i * y5)))));
	elseif (y <= 7e-105)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_2)));
	elseif (y <= 5e+162)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+78], t$95$1, If[LessEqual[y, -3.6e-11], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * t$95$2), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-284], N[(j * N[(t * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b * y4), $MachinePrecision] + N[(N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-105], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+162], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1500000000000001e78 or 4.9999999999999997e162 < y

   1. Initial program 28.5%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

   5. Simplified 69.3%

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

   if -1.1500000000000001e78 < y < -3.59999999999999985e-11

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 77.8%

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

   if -3.59999999999999985e-11 < y < -9.5000000000000003e-284

   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 j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 52.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 57.2%

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

   if -9.5000000000000003e-284 < y < 7e-105

   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 54.1%

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

   if 7e-105 < y < 4.9999999999999997e162

   1. Initial program 27.4%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 49.7%

      \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot \left(\frac{y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)}{t} + \left(b \cdot y4 + \left(\frac{x \cdot \left(i \cdot y1 - b \cdot y0\right)}{t} - i \cdot y5\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

   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 j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 38.5%

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

   6. Taylor expanded in y0 around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 39.0%

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

   8. Simplified 39.0%

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

4. Final simplification 55.8%

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

Alternative 3: 42.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y5 - b \cdot y4\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot t\_1\right)\right)\\ t_3 := x \cdot j - z \cdot k\\ t_4 := b \cdot y0 - i \cdot y1\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot t\_3 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-289}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot t\_4 + t \cdot t\_1\right)\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot t\_3\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(k \cdot t\_4 + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y5) (* b y4)))
        (t_2
         (*
          y
          (+
           (* y3 (- (* c y4) (* a y5)))
           (+ (* x (- (* a b) (* c i))) (* k t_1)))))
        (t_3 (- (* x j) (* z k)))
        (t_4 (- (* b y0) (* i y1))))
   (if (<= y -8.5e+76)
     t_2
     (if (<= y -1.6e-13)
       (*
        i
        (+
         (* c (- (* z t) (* x y)))
         (+ (* y1 t_3) (* y5 (- (* y k) (* t j))))))
       (if (<= y -3e-289)
         (* j (- (* y3 (- (* y0 y5) (* y1 y4))) (+ (* x t_4) (* t t_1))))
         (if (<= y 5.9e-105)
           (*
            y0
            (+
             (* y5 (- (* j y3) (* k y2)))
             (- (* c (- (* x y2) (* z y3))) (* b t_3))))
           (if (<= y 1.5e+162)
             (*
              z
              (+
               (* k t_4)
               (+ (* y3 (- (* a y1) (* c y0))) (* t (- (* c i) (* a b))))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) - (b * y4);
	double t_2 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * t_1)));
	double t_3 = (x * j) - (z * k);
	double t_4 = (b * y0) - (i * y1);
	double tmp;
	if (y <= -8.5e+76) {
		tmp = t_2;
	} else if (y <= -1.6e-13) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_3) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= -3e-289) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * t_4) + (t * t_1)));
	} else if (y <= 5.9e-105) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_3)));
	} else if (y <= 1.5e+162) {
		tmp = z * ((k * t_4) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (i * y5) - (b * y4)
    t_2 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * t_1)))
    t_3 = (x * j) - (z * k)
    t_4 = (b * y0) - (i * y1)
    if (y <= (-8.5d+76)) then
        tmp = t_2
    else if (y <= (-1.6d-13)) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_3) + (y5 * ((y * k) - (t * j)))))
    else if (y <= (-3d-289)) then
        tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * t_4) + (t * t_1)))
    else if (y <= 5.9d-105) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_3)))
    else if (y <= 1.5d+162) then
        tmp = z * ((k * t_4) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y5) - (b * y4);
	double t_2 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * t_1)));
	double t_3 = (x * j) - (z * k);
	double t_4 = (b * y0) - (i * y1);
	double tmp;
	if (y <= -8.5e+76) {
		tmp = t_2;
	} else if (y <= -1.6e-13) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_3) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= -3e-289) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * t_4) + (t * t_1)));
	} else if (y <= 5.9e-105) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_3)));
	} else if (y <= 1.5e+162) {
		tmp = z * ((k * t_4) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y5) - (b * y4)
	t_2 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * t_1)))
	t_3 = (x * j) - (z * k)
	t_4 = (b * y0) - (i * y1)
	tmp = 0
	if y <= -8.5e+76:
		tmp = t_2
	elif y <= -1.6e-13:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_3) + (y5 * ((y * k) - (t * j)))))
	elif y <= -3e-289:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * t_4) + (t * t_1)))
	elif y <= 5.9e-105:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_3)))
	elif y <= 1.5e+162:
		tmp = z * ((k * t_4) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y5) - Float64(b * y4))
	t_2 = Float64(y * Float64(Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(k * t_1))))
	t_3 = Float64(Float64(x * j) - Float64(z * k))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	tmp = 0.0
	if (y <= -8.5e+76)
		tmp = t_2;
	elseif (y <= -1.6e-13)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * t_3) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y <= -3e-289)
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(Float64(x * t_4) + Float64(t * t_1))));
	elseif (y <= 5.9e-105)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(b * t_3))));
	elseif (y <= 1.5e+162)
		tmp = Float64(z * Float64(Float64(k * t_4) + Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y5) - (b * y4);
	t_2 = y * ((y3 * ((c * y4) - (a * y5))) + ((x * ((a * b) - (c * i))) + (k * t_1)));
	t_3 = (x * j) - (z * k);
	t_4 = (b * y0) - (i * y1);
	tmp = 0.0;
	if (y <= -8.5e+76)
		tmp = t_2;
	elseif (y <= -1.6e-13)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_3) + (y5 * ((y * k) - (t * j)))));
	elseif (y <= -3e-289)
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * t_4) + (t * t_1)));
	elseif (y <= 5.9e-105)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_3)));
	elseif (y <= 1.5e+162)
		tmp = z * ((k * t_4) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+76], t$95$2, If[LessEqual[y, -1.6e-13], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * t$95$3), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-289], N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * t$95$4), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-105], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+162], N[(z * N[(N[(k * t$95$4), $MachinePrecision] + N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.49999999999999992e76 or 1.4999999999999999e162 < y

   1. Initial program 28.5%

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

   3. Taylor expanded in y around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

   5. Simplified 69.3%

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

   if -8.49999999999999992e76 < y < -1.6e-13

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 77.8%

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

   if -1.6e-13 < y < -2.9999999999999998e-289

   1. Initial program 26.4%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.3%

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

   if -2.9999999999999998e-289 < y < 5.8999999999999997e-105

   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 53.2%

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

   if 5.8999999999999997e-105 < y < 1.4999999999999999e162

   1. Initial program 27.4%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 49.7%

      \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-289}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ t_2 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot t\_2 + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+149}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot t\_2 - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (-
           (* y3 (- (* y0 y5) (* y1 y4)))
           (+ (* x (- (* b y0) (* i y1))) (* t (- (* i y5) (* b y4)))))))
        (t_2 (- (* x y2) (* z y3))))
   (if (<= j -8.5e+107)
     t_1
     (if (<= j -6.5e+50)
       (*
        t
        (+
         (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
         (* y2 (- (* a y5) (* c y4)))))
       (if (<= j -8.2e-306)
         (*
          c
          (+
           (* i (- (* z t) (* x y)))
           (+ (* y0 t_2) (* y4 (- (* y y3) (* t y2))))))
         (if (<= j 1.9e-188)
           (* b (* a (- (* x y) (* z t))))
           (if (<= j 7e+149)
             (*
              y0
              (+
               (* y5 (- (* j y3) (* k y2)))
               (- (* c t_2) (* b (- (* x j) (* z k))))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double t_2 = (x * y2) - (z * y3);
	double tmp;
	if (j <= -8.5e+107) {
		tmp = t_1;
	} else if (j <= -6.5e+50) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -8.2e-306) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 1.9e-188) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 7e+149) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * t_2) - (b * ((x * j) - (z * k)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
    t_2 = (x * y2) - (z * y3)
    if (j <= (-8.5d+107)) then
        tmp = t_1
    else if (j <= (-6.5d+50)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= (-8.2d-306)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * ((y * y3) - (t * y2)))))
    else if (j <= 1.9d-188) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= 7d+149) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * t_2) - (b * ((x * j) - (z * k)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double t_2 = (x * y2) - (z * y3);
	double tmp;
	if (j <= -8.5e+107) {
		tmp = t_1;
	} else if (j <= -6.5e+50) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -8.2e-306) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 1.9e-188) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 7e+149) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * t_2) - (b * ((x * j) - (z * k)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
	t_2 = (x * y2) - (z * y3)
	tmp = 0
	if j <= -8.5e+107:
		tmp = t_1
	elif j <= -6.5e+50:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	elif j <= -8.2e-306:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * ((y * y3) - (t * y2)))))
	elif j <= 1.9e-188:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= 7e+149:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * t_2) - (b * ((x * j) - (z * k)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(Float64(x * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (j <= -8.5e+107)
		tmp = t_1;
	elseif (j <= -6.5e+50)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -8.2e-306)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_2) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (j <= 1.9e-188)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 7e+149)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(Float64(c * t_2) - Float64(b * Float64(Float64(x * j) - Float64(z * k))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	t_2 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (j <= -8.5e+107)
		tmp = t_1;
	elseif (j <= -6.5e+50)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= -8.2e-306)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * ((y * y3) - (t * y2)))));
	elseif (j <= 1.9e-188)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= 7e+149)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * t_2) - (b * ((x * j) - (z * k)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e+107], t$95$1, If[LessEqual[j, -6.5e+50], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.2e-306], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$2), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e-188], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+149], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * t$95$2), $MachinePrecision] - N[(b * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.4999999999999999e107 or 7.00000000000000023e149 < j

   1. Initial program 26.1%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 61.9%

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

   if -8.4999999999999999e107 < j < -6.5000000000000003e50

   1. Initial program 8.3%

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

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 83.9%

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

   if -6.5000000000000003e50 < j < -8.19999999999999969e-306

   1. Initial program 38.2%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 49.9%

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

   if -8.19999999999999969e-306 < j < 1.9e-188

   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 b around inf

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

   5. Simplified 39.1%

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

   6. Taylor expanded in a around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 51.1%

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

   8. Simplified 51.1%

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

   if 1.9e-188 < j < 7.00000000000000023e149

   1. Initial program 29.0%

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

   3. Taylor expanded in y0 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

   5. Simplified 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+149}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{if}\;j \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -2.95 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - y0 \cdot y3\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (-
           (* y3 (- (* y0 y5) (* y1 y4)))
           (+ (* x (- (* b y0) (* i y1))) (* t (- (* i y5) (* b y4))))))))
   (if (<= j -2.3e+107)
     t_1
     (if (<= j -9e+49)
       (*
        t
        (+
         (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
         (* y2 (- (* a y5) (* c y4)))))
       (if (<= j -2.95e-304)
         (*
          c
          (+
           (* i (- (* z t) (* x y)))
           (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2))))))
         (if (<= j 3.2e-72)
           (*
            x
            (+
             (* y (- (* a b) (* c i)))
             (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0))))))
           (if (<= j 8.8e+139)
             (* c (- (* z (- 0.0 (* y0 y3))) (* t (* y2 y4))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -2.3e+107) {
		tmp = t_1;
	} else if (j <= -9e+49) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -2.95e-304) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 3.2e-72) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (j <= 8.8e+139) {
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
    if (j <= (-2.3d+107)) then
        tmp = t_1
    else if (j <= (-9d+49)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= (-2.95d-304)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
    else if (j <= 3.2d-72) then
        tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
    else if (j <= 8.8d+139) then
        tmp = c * ((z * (0.0d0 - (y0 * y3))) - (t * (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -2.3e+107) {
		tmp = t_1;
	} else if (j <= -9e+49) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -2.95e-304) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 3.2e-72) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (j <= 8.8e+139) {
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
	tmp = 0
	if j <= -2.3e+107:
		tmp = t_1
	elif j <= -9e+49:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	elif j <= -2.95e-304:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
	elif j <= 3.2e-72:
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
	elif j <= 8.8e+139:
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(Float64(x * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	tmp = 0.0
	if (j <= -2.3e+107)
		tmp = t_1;
	elseif (j <= -9e+49)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -2.95e-304)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (j <= 3.2e-72)
		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 (j <= 8.8e+139)
		tmp = Float64(c * Float64(Float64(z * Float64(0.0 - Float64(y0 * y3))) - Float64(t * Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	tmp = 0.0;
	if (j <= -2.3e+107)
		tmp = t_1;
	elseif (j <= -9e+49)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= -2.95e-304)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	elseif (j <= 3.2e-72)
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	elseif (j <= 8.8e+139)
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.3e+107], t$95$1, If[LessEqual[j, -9e+49], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.95e-304], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-72], 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[j, 8.8e+139], N[(c * N[(N[(z * N[(0.0 - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.3e107 or 8.7999999999999998e139 < j

   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 j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 61.2%

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

   if -2.3e107 < j < -8.99999999999999965e49

   1. Initial program 8.3%

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

   3. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 83.9%

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

   if -8.99999999999999965e49 < j < -2.95e-304

   1. Initial program 38.2%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 49.9%

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

   if -2.95e-304 < j < 3.19999999999999999e-72

   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 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 46.8%

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

   if 3.19999999999999999e-72 < j < 8.7999999999999998e139

   1. Initial program 28.0%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 40.7%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

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

       8. *-commutative N/A

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

       9. *-lowering-*.f64 49.9%

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

   11. Simplified 49.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]
   13. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(0 - y0 \cdot \left(y3 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \left(y0 \cdot \left(y3 \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \left(\left(y0 \cdot y3\right) \cdot z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(y0 \cdot y3\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(y3 \cdot y0\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       7. *-lowering-*.f64 57.2%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y0\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

   14. Simplified 57.2%

       \[\leadsto c \cdot \left(\color{blue}{\left(0 - \left(y3 \cdot y0\right) \cdot z\right)} - t \cdot \left(y4 \cdot y2\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -2.95 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - y0 \cdot y3\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ \mathbf{if}\;y5 \leq -5.5 \cdot 10^{+112}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t\_1\right)\right)\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-73}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot t\_1 + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.22 \cdot 10^{-246}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2))))
   (if (<= y5 -5.5e+112)
     (*
      y5
      (+ (* i (- (* y k) (* t j))) (+ (* a (- (* t y2) (* y y3))) (* y0 t_1))))
     (if (<= y5 -1.12e-73)
       (*
        y0
        (+
         (* y5 t_1)
         (- (* c (- (* x y2) (* z y3))) (* b (- (* x j) (* z k))))))
       (if (<= y5 -1.22e-246)
         (*
          y4
          (+
           (* b (- (* t j) (* y k)))
           (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t y2))))))
         (if (<= y5 3.3e+19)
           (*
            z
            (+
             (* k (- (* b y0) (* i y1)))
             (+ (* y3 (- (* a y1) (* c y0))) (* t (- (* c i) (* a b))))))
           (* j (* y0 (- (* y3 y5) (* x b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double tmp;
	if (y5 <= -5.5e+112) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	} else if (y5 <= -1.12e-73) {
		tmp = y0 * ((y5 * t_1) + ((c * ((x * y2) - (z * y3))) - (b * ((x * j) - (z * k)))));
	} else if (y5 <= -1.22e-246) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else if (y5 <= 3.3e+19) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * y3) - (k * y2)
    if (y5 <= (-5.5d+112)) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
    else if (y5 <= (-1.12d-73)) then
        tmp = y0 * ((y5 * t_1) + ((c * ((x * y2) - (z * y3))) - (b * ((x * j) - (z * k)))))
    else if (y5 <= (-1.22d-246)) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
    else if (y5 <= 3.3d+19) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
    else
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double tmp;
	if (y5 <= -5.5e+112) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	} else if (y5 <= -1.12e-73) {
		tmp = y0 * ((y5 * t_1) + ((c * ((x * y2) - (z * y3))) - (b * ((x * j) - (z * k)))));
	} else if (y5 <= -1.22e-246) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else if (y5 <= 3.3e+19) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	} else {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y3) - (k * y2)
	tmp = 0
	if y5 <= -5.5e+112:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
	elif y5 <= -1.12e-73:
		tmp = y0 * ((y5 * t_1) + ((c * ((x * y2) - (z * y3))) - (b * ((x * j) - (z * k)))))
	elif y5 <= -1.22e-246:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
	elif y5 <= 3.3e+19:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))))
	else:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y3) - Float64(k * y2))
	tmp = 0.0
	if (y5 <= -5.5e+112)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_1))));
	elseif (y5 <= -1.12e-73)
		tmp = Float64(y0 * Float64(Float64(y5 * t_1) + Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(b * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (y5 <= -1.22e-246)
		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))))));
	elseif (y5 <= 3.3e+19)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))));
	else
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y3) - (k * y2);
	tmp = 0.0;
	if (y5 <= -5.5e+112)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	elseif (y5 <= -1.12e-73)
		tmp = y0 * ((y5 * t_1) + ((c * ((x * y2) - (z * y3))) - (b * ((x * j) - (z * k)))));
	elseif (y5 <= -1.22e-246)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	elseif (y5 <= 3.3e+19)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * ((a * y1) - (c * y0))) + (t * ((c * i) - (a * b)))));
	else
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.5e+112], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.12e-73], N[(y0 * N[(N[(y5 * t$95$1), $MachinePrecision] + N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.22e-246], 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], If[LessEqual[y5, 3.3e+19], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -5.50000000000000026e112

   1. Initial program 22.7%

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

   3. Taylor expanded in 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 68.2%

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

   if -5.50000000000000026e112 < y5 < -1.11999999999999995e-73

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 51.9%

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

   if -1.11999999999999995e-73 < y5 < -1.2200000000000001e-246

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 56.0%

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

   if -1.2200000000000001e-246 < y5 < 3.3e19

   1. Initial program 38.2%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 49.0%

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

   if 3.3e19 < y5

   1. Initial program 17.8%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 54.4%

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

   6. Taylor expanded in y0 around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 57.9%

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

   8. Simplified 57.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.5 \cdot 10^{+112}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-73}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.22 \cdot 10^{-246}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot j - z \cdot k\\ \mathbf{if}\;y0 \leq -9.6 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{-73}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot t\_1 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 38000:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= y0 -9.6e+166)
     (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
     (if (<= y0 -1.35e-73)
       (*
        y3
        (+
         (* j (- (* y0 y5) (* y1 y4)))
         (+ (* y (- (* c y4) (* a y5))) (* z (- (* a y1) (* c y0))))))
       (if (<= y0 2.35e-281)
         (*
          i
          (+
           (* c (- (* z t) (* x y)))
           (+ (* y1 t_1) (* y5 (- (* y k) (* t j))))))
         (if (<= y0 38000.0)
           (*
            t
            (+
             (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
             (* y2 (- (* a y5) (* c y4)))))
           (*
            y0
            (+
             (* y5 (- (* j y3) (* k y2)))
             (- (* c (- (* x y2) (* z y3))) (* b t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * j) - (z * k);
	double tmp;
	if (y0 <= -9.6e+166) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y0 <= -1.35e-73) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0)))));
	} else if (y0 <= 2.35e-281) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_1) + (y5 * ((y * k) - (t * j)))));
	} else if (y0 <= 38000.0) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * j) - (z * k)
    if (y0 <= (-9.6d+166)) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else if (y0 <= (-1.35d-73)) then
        tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0)))))
    else if (y0 <= 2.35d-281) then
        tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_1) + (y5 * ((y * k) - (t * j)))))
    else if (y0 <= 38000.0d0) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * j) - (z * k);
	double tmp;
	if (y0 <= -9.6e+166) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y0 <= -1.35e-73) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0)))));
	} else if (y0 <= 2.35e-281) {
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_1) + (y5 * ((y * k) - (t * j)))));
	} else if (y0 <= 38000.0) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * j) - (z * k)
	tmp = 0
	if y0 <= -9.6e+166:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	elif y0 <= -1.35e-73:
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0)))))
	elif y0 <= 2.35e-281:
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_1) + (y5 * ((y * k) - (t * j)))))
	elif y0 <= 38000.0:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (y0 <= -9.6e+166)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	elseif (y0 <= -1.35e-73)
		tmp = Float64(y3 * Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y0 <= 2.35e-281)
		tmp = Float64(i * Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y1 * t_1) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y0 <= 38000.0)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(b * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * j) - (z * k);
	tmp = 0.0;
	if (y0 <= -9.6e+166)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	elseif (y0 <= -1.35e-73)
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0)))));
	elseif (y0 <= 2.35e-281)
		tmp = i * ((c * ((z * t) - (x * y))) + ((y1 * t_1) + (y5 * ((y * k) - (t * j)))));
	elseif (y0 <= 38000.0)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + ((c * ((x * y2) - (z * y3))) - (b * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -9.6e+166], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.35e-73], N[(y3 * N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.35e-281], N[(i * N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y1 * t$95$1), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 38000.0], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -9.59999999999999969e166

   1. Initial program 21.6%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 40.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 37.3%

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

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

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

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

       2. associate-*r* N/A

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

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

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

       4. *-commutative N/A

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

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

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

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

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

       7. associate-/l* N/A

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

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

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

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

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

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

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

       11. *-lowering-*.f64 61.4%

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

   11. Simplified 61.4%

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

   if -9.59999999999999969e166 < y0 < -1.34999999999999997e-73

   1. Initial program 31.7%

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

   3. Taylor expanded in y3 around -inf

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

      1. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 54.2%

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

   if -1.34999999999999997e-73 < y0 < 2.3500000000000001e-281

   1. Initial program 44.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 58.3%

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

   if 2.3500000000000001e-281 < y0 < 38000

   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 t around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   5. Simplified 54.5%

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

   if 38000 < y0

   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 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 52.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot y5\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -9.6 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{-73}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 38000:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{if}\;j \leq -1.52 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - y0 \cdot y3\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (-
           (* y3 (- (* y0 y5) (* y1 y4)))
           (+ (* x (- (* b y0) (* i y1))) (* t (- (* i y5) (* b y4))))))))
   (if (<= j -1.52e+94)
     t_1
     (if (<= j -7.8e-306)
       (*
        c
        (+
         (* i (- (* z t) (* x y)))
         (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2))))))
       (if (<= j 2.3e-70)
         (*
          x
          (+
           (* y (- (* a b) (* c i)))
           (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0))))))
         (if (<= j 8.8e+139)
           (* c (- (* z (- 0.0 (* y0 y3))) (* t (* y2 y4))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -1.52e+94) {
		tmp = t_1;
	} else if (j <= -7.8e-306) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 2.3e-70) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (j <= 8.8e+139) {
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
    if (j <= (-1.52d+94)) then
        tmp = t_1
    else if (j <= (-7.8d-306)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
    else if (j <= 2.3d-70) then
        tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
    else if (j <= 8.8d+139) then
        tmp = c * ((z * (0.0d0 - (y0 * y3))) - (t * (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -1.52e+94) {
		tmp = t_1;
	} else if (j <= -7.8e-306) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	} else if (j <= 2.3e-70) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (j <= 8.8e+139) {
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))))
	tmp = 0
	if j <= -1.52e+94:
		tmp = t_1
	elif j <= -7.8e-306:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))))
	elif j <= 2.3e-70:
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
	elif j <= 8.8e+139:
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) - Float64(Float64(x * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	tmp = 0.0
	if (j <= -1.52e+94)
		tmp = t_1;
	elseif (j <= -7.8e-306)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (j <= 2.3e-70)
		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 (j <= 8.8e+139)
		tmp = Float64(c * Float64(Float64(z * Float64(0.0 - Float64(y0 * y3))) - Float64(t * Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) - ((x * ((b * y0) - (i * y1))) + (t * ((i * y5) - (b * y4)))));
	tmp = 0.0;
	if (j <= -1.52e+94)
		tmp = t_1;
	elseif (j <= -7.8e-306)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2)))));
	elseif (j <= 2.3e-70)
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	elseif (j <= 8.8e+139)
		tmp = c * ((z * (0.0 - (y0 * y3))) - (t * (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.52e+94], t$95$1, If[LessEqual[j, -7.8e-306], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-70], 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[j, 8.8e+139], N[(c * N[(N[(z * N[(0.0 - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5199999999999999e94 or 8.7999999999999998e139 < j

   1. Initial program 24.9%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 60.3%

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

   if -1.5199999999999999e94 < j < -7.799999999999999e-306

   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 c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 48.0%

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

   if -7.799999999999999e-306 < j < 2.30000000000000001e-70

   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 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 46.8%

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

   if 2.30000000000000001e-70 < j < 8.7999999999999998e139

   1. Initial program 28.0%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 40.7%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in y around 0

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

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

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

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

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

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

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

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

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

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

       8. *-commutative N/A

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

       9. *-lowering-*.f64 49.9%

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

   11. Simplified 49.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]
   13. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(0 - y0 \cdot \left(y3 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \left(y0 \cdot \left(y3 \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \left(\left(y0 \cdot y3\right) \cdot z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(y0 \cdot y3\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\left(y3 \cdot y0\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

       7. *-lowering-*.f64 57.2%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y0\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

   14. Simplified 57.2%

       \[\leadsto c \cdot \left(\color{blue}{\left(0 - \left(y3 \cdot y0\right) \cdot z\right)} - t \cdot \left(y4 \cdot y2\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.52 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \left(z \cdot \left(0 - y0 \cdot y3\right) - t \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) - \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;y4 \leq -4.6 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot t\_1\\ \mathbf{elif}\;y4 \leq -82000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(\left(x \cdot y2 - z \cdot y3\right) + \frac{y4 \cdot t\_2}{y0}\right)\right)\\ \mathbf{elif}\;y4 \leq -4 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot t\_1 + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot t\_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k))) (t_2 (- (* y y3) (* t y2))))
   (if (<= y4 -4.6e+185)
     (* (* b y4) t_1)
     (if (<= y4 -82000.0)
       (* c (* y0 (+ (- (* x y2) (* z y3)) (/ (* y4 t_2) y0))))
       (if (<= y4 -4e-202)
         (* j (* t (* i (- (* x (/ y1 t)) y5))))
         (if (<= y4 2.4e-5)
           (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
           (*
            y4
            (+ (* b t_1) (+ (* y1 (- (* k y2) (* j y3))) (* c 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 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -4.6e+185) {
		tmp = (b * y4) * t_1;
	} else if (y4 <= -82000.0) {
		tmp = c * (y0 * (((x * y2) - (z * y3)) + ((y4 * t_2) / y0)));
	} else if (y4 <= -4e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 2.4e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = y4 * ((b * t_1) + ((y1 * ((k * y2) - (j * y3))) + (c * 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 = (t * j) - (y * k)
    t_2 = (y * y3) - (t * y2)
    if (y4 <= (-4.6d+185)) then
        tmp = (b * y4) * t_1
    else if (y4 <= (-82000.0d0)) then
        tmp = c * (y0 * (((x * y2) - (z * y3)) + ((y4 * t_2) / y0)))
    else if (y4 <= (-4d-202)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 2.4d-5) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else
        tmp = y4 * ((b * t_1) + ((y1 * ((k * y2) - (j * y3))) + (c * 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 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double tmp;
	if (y4 <= -4.6e+185) {
		tmp = (b * y4) * t_1;
	} else if (y4 <= -82000.0) {
		tmp = c * (y0 * (((x * y2) - (z * y3)) + ((y4 * t_2) / y0)));
	} else if (y4 <= -4e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 2.4e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = y4 * ((b * t_1) + ((y1 * ((k * y2) - (j * y3))) + (c * 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 = (t * j) - (y * k)
	t_2 = (y * y3) - (t * y2)
	tmp = 0
	if y4 <= -4.6e+185:
		tmp = (b * y4) * t_1
	elif y4 <= -82000.0:
		tmp = c * (y0 * (((x * y2) - (z * y3)) + ((y4 * t_2) / y0)))
	elif y4 <= -4e-202:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 2.4e-5:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	else:
		tmp = y4 * ((b * t_1) + ((y1 * ((k * y2) - (j * y3))) + (c * 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(t * j) - Float64(y * k))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (y4 <= -4.6e+185)
		tmp = Float64(Float64(b * y4) * t_1);
	elseif (y4 <= -82000.0)
		tmp = Float64(c * Float64(y0 * Float64(Float64(Float64(x * y2) - Float64(z * y3)) + Float64(Float64(y4 * t_2) / y0))));
	elseif (y4 <= -4e-202)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 2.4e-5)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	else
		tmp = Float64(y4 * Float64(Float64(b * t_1) + Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * 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 = (t * j) - (y * k);
	t_2 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (y4 <= -4.6e+185)
		tmp = (b * y4) * t_1;
	elseif (y4 <= -82000.0)
		tmp = c * (y0 * (((x * y2) - (z * y3)) + ((y4 * t_2) / y0)));
	elseif (y4 <= -4e-202)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 2.4e-5)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	else
		tmp = y4 * ((b * t_1) + ((y1 * ((k * y2) - (j * y3))) + (c * 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[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.6e+185], N[(N[(b * y4), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y4, -82000.0], N[(c * N[(y0 * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$2), $MachinePrecision] / y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4e-202], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.4e-5], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(b * t$95$1), $MachinePrecision] + N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -4.6000000000000003e185

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.2%

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

   6. Taylor expanded in y4 around inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      6. *-lowering-*.f64 53.4%

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

   8. Simplified 53.4%

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

   if -4.6000000000000003e185 < y4 < -82000

   1. Initial program 23.5%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 44.9%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 53.8%

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

   8. Simplified 53.8%

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

   9. Taylor expanded in y0 around -inf

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

       1. mul-1-neg N/A

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

       2. *-commutative N/A

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

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

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

       4. neg-mul-1 N/A

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

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

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

   11. Simplified 53.9%

       \[\leadsto c \cdot \color{blue}{\left(\left(\frac{y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)}{y0} - \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot \left(0 - y0\right)\right)} \]

   if -82000 < y4 < -4.0000000000000001e-202

   1. Initial program 36.5%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

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

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

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

   if -4.0000000000000001e-202 < y4 < 2.4000000000000001e-5

   1. Initial program 27.4%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 37.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 38.6%

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

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

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

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

       2. associate-*r* N/A

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

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

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

       4. *-commutative N/A

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

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

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

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

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

       7. associate-/l* N/A

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

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

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

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

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

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

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

       11. *-lowering-*.f64 46.0%

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

   11. Simplified 46.0%

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

   if 2.4000000000000001e-5 < y4

   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 59.1%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.6 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -82000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(\left(x \cdot y2 - z \cdot y3\right) + \frac{y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0}\right)\right)\\ \mathbf{elif}\;y4 \leq -4 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y4 \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -170000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(\left(x \cdot y2 - z \cdot y3\right) + \frac{t\_1}{y0}\right)\right)\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (- (* y y3) (* t y2)))))
   (if (<= y4 -1.36e+188)
     (* (* b y4) (- (* t j) (* y k)))
     (if (<= y4 -170000.0)
       (* c (* y0 (+ (- (* x y2) (* z y3)) (/ t_1 y0))))
       (if (<= y4 -9.5e-202)
         (* j (* t (* i (- (* x (/ y1 t)) y5))))
         (if (<= y4 3.5e-5)
           (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
           (* c (+ (* i (- (* z t) (* x y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -1.36e+188) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -170000.0) {
		tmp = c * (y0 * (((x * y2) - (z * y3)) + (t_1 / y0)));
	} else if (y4 <= -9.5e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 3.5e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * ((y * y3) - (t * y2))
    if (y4 <= (-1.36d+188)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-170000.0d0)) then
        tmp = c * (y0 * (((x * y2) - (z * y3)) + (t_1 / y0)))
    else if (y4 <= (-9.5d-202)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 3.5d-5) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else
        tmp = c * ((i * ((z * t) - (x * y))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -1.36e+188) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -170000.0) {
		tmp = c * (y0 * (((x * y2) - (z * y3)) + (t_1 / y0)));
	} else if (y4 <= -9.5e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 3.5e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * ((y * y3) - (t * y2))
	tmp = 0
	if y4 <= -1.36e+188:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -170000.0:
		tmp = c * (y0 * (((x * y2) - (z * y3)) + (t_1 / y0)))
	elif y4 <= -9.5e-202:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 3.5e-5:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	else:
		tmp = c * ((i * ((z * t) - (x * y))) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y4 <= -1.36e+188)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -170000.0)
		tmp = Float64(c * Float64(y0 * Float64(Float64(Float64(x * y2) - Float64(z * y3)) + Float64(t_1 / y0))));
	elseif (y4 <= -9.5e-202)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 3.5e-5)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	else
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y4 <= -1.36e+188)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -170000.0)
		tmp = c * (y0 * (((x * y2) - (z * y3)) + (t_1 / y0)));
	elseif (y4 <= -9.5e-202)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 3.5e-5)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	else
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.36e+188], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -170000.0], N[(c * N[(y0 * N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9.5e-202], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.5e-5], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.36e188

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.2%

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

   6. Taylor expanded in y4 around inf

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

      1. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      6. *-lowering-*.f64 53.4%

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

   8. Simplified 53.4%

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

   if -1.36e188 < y4 < -1.7e5

   1. Initial program 23.5%

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

   3. Taylor expanded in c around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 44.9%

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

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-lowering-*.f64 53.8%

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

   8. Simplified 53.8%

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

   9. Taylor expanded in y0 around -inf

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

       1. mul-1-neg N/A

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

       2. *-commutative N/A

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

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

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

       4. neg-mul-1 N/A

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

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

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

   11. Simplified 53.9%

       \[\leadsto c \cdot \color{blue}{\left(\left(\frac{y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)}{y0} - \left(x \cdot y2 - y3 \cdot z\right)\right) \cdot \left(0 - y0\right)\right)} \]

   if -1.7e5 < y4 < -9.5000000000000001e-202

   1. Initial program 36.5%

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

   3. Taylor expanded in j around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)}\right)\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \color{blue}{-1 \cdot y5}\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)}\right) \]

   if -9.5000000000000001e-202 < y4 < 3.4999999999999997e-5

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(t \cdot y0\right) \cdot \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(t \cdot y0\right), \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(y0 \cdot t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(\frac{y3 \cdot y5}{t}\right), \color{blue}{\left(\frac{b \cdot x}{t}\right)}\right)\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(y3 \cdot \frac{y5}{t}\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \left(\frac{y5}{t}\right)\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \left(\frac{b \cdot \color{blue}{x}}{t}\right)\right)\right)\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\left(b \cdot x\right), \color{blue}{t}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 46.0%

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), t\right)\right)\right)\right) \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot t\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{b \cdot x}{t}\right)\right)} \]

   if 3.4999999999999997e-5 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y0 around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(i\right)\right), \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-i\right) \cdot \left(x \cdot y - t \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -170000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(\left(x \cdot y2 - z \cdot y3\right) + \frac{y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0}\right)\right)\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -2800000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + t\_1\right)\\ \mathbf{elif}\;y4 \leq -5.8 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (- (* y y3) (* t y2)))))
   (if (<= y4 -1.85e+189)
     (* (* b y4) (- (* t j) (* y k)))
     (if (<= y4 -2800000.0)
       (* c (+ (* y0 (- (* x y2) (* z y3))) t_1))
       (if (<= y4 -5.8e-202)
         (* j (* t (* i (- (* x (/ y1 t)) y5))))
         (if (<= y4 1.5e-5)
           (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
           (* c (+ (* i (- (* z t) (* x y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -1.85e+189) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -2800000.0) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + t_1);
	} else if (y4 <= -5.8e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 1.5e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * ((y * y3) - (t * y2))
    if (y4 <= (-1.85d+189)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-2800000.0d0)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + t_1)
    else if (y4 <= (-5.8d-202)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 1.5d-5) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else
        tmp = c * ((i * ((z * t) - (x * y))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((y * y3) - (t * y2));
	double tmp;
	if (y4 <= -1.85e+189) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -2800000.0) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + t_1);
	} else if (y4 <= -5.8e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 1.5e-5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else {
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * ((y * y3) - (t * y2))
	tmp = 0
	if y4 <= -1.85e+189:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -2800000.0:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + t_1)
	elif y4 <= -5.8e-202:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 1.5e-5:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	else:
		tmp = c * ((i * ((z * t) - (x * y))) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y4 <= -1.85e+189)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -2800000.0)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + t_1));
	elseif (y4 <= -5.8e-202)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 1.5e-5)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	else
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y4 <= -1.85e+189)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -2800000.0)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + t_1);
	elseif (y4 <= -5.8e-202)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 1.5e-5)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	else
		tmp = c * ((i * ((z * t) - (x * y))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.85e+189], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2800000.0], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.8e-202], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.5e-5], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.8500000000000001e189

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{j \cdot t} - k \cdot y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

   if -1.8500000000000001e189 < y4 < -2.8e6

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -2.8e6 < y4 < -5.79999999999999976e-202

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)}\right)\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \color{blue}{-1 \cdot y5}\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)}\right) \]

   if -5.79999999999999976e-202 < y4 < 1.50000000000000004e-5

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 38.6%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(t \cdot y0\right) \cdot \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(t \cdot y0\right), \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(y0 \cdot t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(\frac{y3 \cdot y5}{t}\right), \color{blue}{\left(\frac{b \cdot x}{t}\right)}\right)\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(y3 \cdot \frac{y5}{t}\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \left(\frac{y5}{t}\right)\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \left(\frac{b \cdot \color{blue}{x}}{t}\right)\right)\right)\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\left(b \cdot x\right), \color{blue}{t}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 46.0%

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), t\right)\right)\right)\right) \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot t\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{b \cdot x}{t}\right)\right)} \]

   if 1.50000000000000004e-5 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y0 around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(i\right)\right), \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-i\right) \cdot \left(x \cdot y - t \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -2800000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -5.8 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.5 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -280000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -4 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.2:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{+251}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -3.6e+186)
   (* (* b y4) (- (* t j) (* y k)))
   (if (<= y4 -280000.0)
     (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
     (if (<= y4 -4e-203)
       (* j (* t (* i (- (* x (/ y1 t)) y5))))
       (if (<= y4 6.2)
         (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
         (if (<= y4 1.7e+251)
           (* c (* t (- (* z i) (* y2 y4))))
           (* c (* y (* y3 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.6e+186) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -280000.0) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y4 <= -4e-203) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 6.2) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y4 <= 1.7e+251) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-3.6d+186)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-280000.0d0)) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else if (y4 <= (-4d-203)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 6.2d0) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else if (y4 <= 1.7d+251) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.6e+186) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -280000.0) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y4 <= -4e-203) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 6.2) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y4 <= 1.7e+251) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -3.6e+186:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -280000.0:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	elif y4 <= -4e-203:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 6.2:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	elif y4 <= 1.7e+251:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -3.6e+186)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -280000.0)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y4 <= -4e-203)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 6.2)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	elseif (y4 <= 1.7e+251)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -3.6e+186)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -280000.0)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y4 <= -4e-203)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 6.2)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	elseif (y4 <= 1.7e+251)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -3.6e+186], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -280000.0], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4e-203], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.2], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.7e+251], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -3.6000000000000002e186

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{j \cdot t} - k \cdot y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

   if -3.6000000000000002e186 < y4 < -2.8e5

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -2.8e5 < y4 < -4.0000000000000001e-203

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)}\right)\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \color{blue}{-1 \cdot y5}\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)}\right) \]

   if -4.0000000000000001e-203 < y4 < 6.20000000000000018

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 38.8%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(t \cdot y0\right) \cdot \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(t \cdot y0\right), \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(y0 \cdot t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(\frac{y3 \cdot y5}{t}\right), \color{blue}{\left(\frac{b \cdot x}{t}\right)}\right)\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(y3 \cdot \frac{y5}{t}\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \left(\frac{y5}{t}\right)\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \left(\frac{b \cdot \color{blue}{x}}{t}\right)\right)\right)\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\left(b \cdot x\right), \color{blue}{t}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 46.1%

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), t\right)\right)\right)\right) \]

   11. Simplified 46.1%

       \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot t\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{b \cdot x}{t}\right)\right)} \]

   if 6.20000000000000018 < y4 < 1.70000000000000006e251

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 1.70000000000000006e251 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 60.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -280000:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -4 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.2:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y4 \leq 1.7 \cdot 10^{+251}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.22 \cdot 10^{+184}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -310000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 10.5:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+251}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.22e+184)
   (* (* b y4) (- (* t j) (* y k)))
   (if (<= y4 -310000.0)
     (* c (* y4 (- (* y y3) (* t y2))))
     (if (<= y4 -1.05e-202)
       (* j (* t (* i (- (* x (/ y1 t)) y5))))
       (if (<= y4 10.5)
         (* j (* (* t y0) (- (* y3 (/ y5 t)) (/ (* x b) t))))
         (if (<= y4 9.5e+251)
           (* c (* t (- (* z i) (* y2 y4))))
           (* c (* y (* y3 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.22e+184) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -310000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= -1.05e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 10.5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y4 <= 9.5e+251) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.22d+184)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-310000.0d0)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y4 <= (-1.05d-202)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 10.5d0) then
        tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
    else if (y4 <= 9.5d+251) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.22e+184) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -310000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= -1.05e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 10.5) {
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	} else if (y4 <= 9.5e+251) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.22e+184:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -310000.0:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y4 <= -1.05e-202:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 10.5:
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)))
	elif y4 <= 9.5e+251:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.22e+184)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -310000.0)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y4 <= -1.05e-202)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 10.5)
		tmp = Float64(j * Float64(Float64(t * y0) * Float64(Float64(y3 * Float64(y5 / t)) - Float64(Float64(x * b) / t))));
	elseif (y4 <= 9.5e+251)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.22e+184)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -310000.0)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y4 <= -1.05e-202)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 10.5)
		tmp = j * ((t * y0) * ((y3 * (y5 / t)) - ((x * b) / t)));
	elseif (y4 <= 9.5e+251)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.22e+184], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -310000.0], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.05e-202], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 10.5], N[(j * N[(N[(t * y0), $MachinePrecision] * N[(N[(y3 * N[(y5 / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.5e+251], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.22000000000000006e184

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{j \cdot t} - k \cdot y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

   if -1.22000000000000006e184 < y4 < -3.1e5

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -3.1e5 < y4 < -1.04999999999999993e-202

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)}\right)\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \color{blue}{-1 \cdot y5}\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)}\right) \]

   if -1.04999999999999993e-202 < y4 < 10.5

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 38.8%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{j \cdot \left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(y0 \cdot \left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(\left(t \cdot y0\right) \cdot \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(t \cdot y0\right), \color{blue}{\left(\frac{y3 \cdot y5}{t} - \frac{b \cdot x}{t}\right)}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\left(y0 \cdot t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \left(\color{blue}{\frac{y3 \cdot y5}{t}} - \frac{b \cdot x}{t}\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(\frac{y3 \cdot y5}{t}\right), \color{blue}{\left(\frac{b \cdot x}{t}\right)}\right)\right)\right) \]

       7. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\left(y3 \cdot \frac{y5}{t}\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \left(\frac{y5}{t}\right)\right), \left(\frac{\color{blue}{b \cdot x}}{t}\right)\right)\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \left(\frac{b \cdot \color{blue}{x}}{t}\right)\right)\right)\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\left(b \cdot x\right), \color{blue}{t}\right)\right)\right)\right) \]

       11. *-lowering-*.f64 46.1%

           \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y0, t\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, \mathsf{/.f64}\left(y5, t\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, x\right), t\right)\right)\right)\right) \]

   11. Simplified 46.1%

       \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot t\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{b \cdot x}{t}\right)\right)} \]

   if 10.5 < y4 < 9.49999999999999931e251

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 9.49999999999999931e251 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 60.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.22 \cdot 10^{+184}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -310000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.05 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 10.5:\\ \;\;\;\;j \cdot \left(\left(t \cdot y0\right) \cdot \left(y3 \cdot \frac{y5}{t} - \frac{x \cdot b}{t}\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{+251}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+181}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -1750000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.75 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -4.8e+181)
   (* (* b y4) (- (* t j) (* y k)))
   (if (<= y4 -1750000.0)
     (* c (* y4 (- (* y y3) (* t y2))))
     (if (<= y4 -1.75e-202)
       (* j (* t (* i (- (* x (/ y1 t)) y5))))
       (if (<= y4 2.9e-5)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (if (<= y4 2.5e+252)
           (* c (* t (- (* z i) (* y2 y4))))
           (* c (* y (* y3 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -4.8e+181) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -1750000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= -1.75e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 2.9e-5) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y4 <= 2.5e+252) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-4.8d+181)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-1750000.0d0)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y4 <= (-1.75d-202)) then
        tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
    else if (y4 <= 2.9d-5) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y4 <= 2.5d+252) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -4.8e+181) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -1750000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y4 <= -1.75e-202) {
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	} else if (y4 <= 2.9e-5) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y4 <= 2.5e+252) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -4.8e+181:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -1750000.0:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y4 <= -1.75e-202:
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)))
	elif y4 <= 2.9e-5:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y4 <= 2.5e+252:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -4.8e+181)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -1750000.0)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y4 <= -1.75e-202)
		tmp = Float64(j * Float64(t * Float64(i * Float64(Float64(x * Float64(y1 / t)) - y5))));
	elseif (y4 <= 2.9e-5)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y4 <= 2.5e+252)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -4.8e+181)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -1750000.0)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y4 <= -1.75e-202)
		tmp = j * (t * (i * ((x * (y1 / t)) - y5)));
	elseif (y4 <= 2.9e-5)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y4 <= 2.5e+252)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -4.8e+181], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1750000.0], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.75e-202], N[(j * N[(t * N[(i * N[(N[(x * N[(y1 / t), $MachinePrecision]), $MachinePrecision] - y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.9e-5], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.5e+252], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -4.80000000000000004e181

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{j \cdot t} - k \cdot y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

   if -4.80000000000000004e181 < y4 < -1.75e6

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \color{blue}{\left(y \cdot y3 - t \cdot y2\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(y \cdot y3\right), \color{blue}{\left(t \cdot y2\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \left(\color{blue}{t} \cdot y2\right)\right)\right)\right) \]

      4. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, y3\right), \mathsf{*.f64}\left(t, \color{blue}{y2}\right)\right)\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -1.75e6 < y4 < -1.75e-202

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + b \cdot y4\right) - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-1 \cdot \frac{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t}\right), \color{blue}{\left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}{t}\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), t\right), \left(\color{blue}{b \cdot y4} - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(\color{blue}{b} \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\mathsf{neg}\left(y3\right)\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      9. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{neg.f64}\left(y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), t\right), \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)}\right)\right)\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(\frac{\left(-y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}{t} + \left(b \cdot y4 - \left(i \cdot y5 + \frac{x \cdot \left(b \cdot y0 - i \cdot y1\right)}{t}\right)\right)\right)\right)} \]

   9. Taylor expanded in i around -inf

      \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot \left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y5 + \frac{x \cdot y1}{t}\right)}\right)\right)\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \color{blue}{-1 \cdot y5}\right)\right)\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} + \left(\mathsf{neg}\left(y5\right)\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \left(\frac{x \cdot y1}{t} - \color{blue}{y5}\right)\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(\frac{x \cdot y1}{t}\right), \color{blue}{y5}\right)\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(x \cdot \frac{y1}{t}\right), y5\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y1}{t}\right)\right), y5\right)\right)\right)\right) \]

       8. /-lowering-/.f64 52.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y1, t\right)\right), y5\right)\right)\right)\right) \]

   11. Simplified 52.3%

       \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)}\right) \]

   if -1.75e-202 < y4 < 2.9e-5

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 37.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 45.0%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   if 2.9e-5 < y4 < 2.4999999999999998e252

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 56.3%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 2.4999999999999998e252 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 60.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.8 \cdot 10^{+181}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -1750000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.75 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(t \cdot \left(i \cdot \left(x \cdot \frac{y1}{t} - y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+187}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1e+187)
   (* (* b y4) (- (* t j) (* y k)))
   (if (<= y4 -1e+41)
     (* c (* y2 (- 0.0 (* t y4))))
     (if (<= y4 -1.15e-59)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= y4 2.85e-5)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (if (<= y4 3e+252)
           (* c (* t (- (* z i) (* y2 y4))))
           (* c (* y (* y3 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+187) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -1e+41) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y4 <= -1.15e-59) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y4 <= 2.85e-5) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y4 <= 3e+252) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1d+187)) then
        tmp = (b * y4) * ((t * j) - (y * k))
    else if (y4 <= (-1d+41)) then
        tmp = c * (y2 * (0.0d0 - (t * y4)))
    else if (y4 <= (-1.15d-59)) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (y4 <= 2.85d-5) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y4 <= 3d+252) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = c * (y * (y3 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+187) {
		tmp = (b * y4) * ((t * j) - (y * k));
	} else if (y4 <= -1e+41) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y4 <= -1.15e-59) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y4 <= 2.85e-5) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y4 <= 3e+252) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = c * (y * (y3 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1e+187:
		tmp = (b * y4) * ((t * j) - (y * k))
	elif y4 <= -1e+41:
		tmp = c * (y2 * (0.0 - (t * y4)))
	elif y4 <= -1.15e-59:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif y4 <= 2.85e-5:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y4 <= 3e+252:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = c * (y * (y3 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1e+187)
		tmp = Float64(Float64(b * y4) * Float64(Float64(t * j) - Float64(y * k)));
	elseif (y4 <= -1e+41)
		tmp = Float64(c * Float64(y2 * Float64(0.0 - Float64(t * y4))));
	elseif (y4 <= -1.15e-59)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (y4 <= 2.85e-5)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y4 <= 3e+252)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1e+187)
		tmp = (b * y4) * ((t * j) - (y * k));
	elseif (y4 <= -1e+41)
		tmp = c * (y2 * (0.0 - (t * y4)));
	elseif (y4 <= -1.15e-59)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (y4 <= 2.85e-5)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y4 <= 3e+252)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = c * (y * (y3 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1e+187], N[(N[(b * y4), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1e+41], N[(c * N[(y2 * N[(0.0 - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.15e-59], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.85e-5], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3e+252], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -9.99999999999999907e186

   1. Initial program 36.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 41.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(b \cdot y4\right) \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{j \cdot t} - k \cdot y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\left(j \cdot t\right), \color{blue}{\left(k \cdot y\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \left(\color{blue}{k} \cdot y\right)\right)\right) \]

      6. *-lowering-*.f64 53.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, t\right), \mathsf{*.f64}\left(k, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 53.4%

      \[\leadsto \color{blue}{\left(b \cdot y4\right) \cdot \left(j \cdot t - k \cdot y\right)} \]

   if -9.99999999999999907e186 < y4 < -1.00000000000000001e41

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 59.1%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 59.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 42.8%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 42.8%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y4\right) \cdot y2\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\mathsf{neg}\left(\color{blue}{y2}\right)\right)\right)\right) \]

       6. neg-lowering-neg.f64 54.6%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{neg.f64}\left(y2\right)\right)\right) \]

   13. Applied egg-rr 54.6%

       \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)} \]

   if -1.00000000000000001e41 < y4 < -1.1499999999999999e-59

   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 z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot z\right) \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-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. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(t \cdot c\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, c\right), \left(\color{blue}{k} \cdot y1\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, c\right), \left(y1 \cdot \color{blue}{k}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 46.6%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, c\right), \mathsf{*.f64}\left(y1, \color{blue}{k}\right)\right)\right)\right) \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(t \cdot c - y1 \cdot k\right)\right)} \]

   if -1.1499999999999999e-59 < y4 < 2.8500000000000002e-5

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 41.6%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   if 2.8500000000000002e-5 < y4 < 2.99999999999999989e252

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 56.3%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 2.99999999999999989e252 < y4

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 53.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 53.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 60.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+187}:\\ \;\;\;\;\left(b \cdot y4\right) \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{elif}\;y4 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 3 \cdot 10^{+252}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -2.25 \cdot 10^{+153}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y3 \leq -1.55 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 3 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 64000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= y3 -2.25e+153)
     (* (* z (* y0 y3)) (- 0.0 c))
     (if (<= y3 -1.55e-270)
       t_1
       (if (<= y3 3e-224)
         (* b (* a (- (* x y) (* z t))))
         (if (<= y3 64000000000000.0)
           t_1
           (* c (* y0 (- (* x y2) (* 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) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -2.25e+153) {
		tmp = (z * (y0 * y3)) * (0.0 - c);
	} else if (y3 <= -1.55e-270) {
		tmp = t_1;
	} else if (y3 <= 3e-224) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 64000000000000.0) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    if (y3 <= (-2.25d+153)) then
        tmp = (z * (y0 * y3)) * (0.0d0 - c)
    else if (y3 <= (-1.55d-270)) then
        tmp = t_1
    else if (y3 <= 3d-224) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y3 <= 64000000000000.0d0) then
        tmp = t_1
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -2.25e+153) {
		tmp = (z * (y0 * y3)) * (0.0 - c);
	} else if (y3 <= -1.55e-270) {
		tmp = t_1;
	} else if (y3 <= 3e-224) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 64000000000000.0) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if y3 <= -2.25e+153:
		tmp = (z * (y0 * y3)) * (0.0 - c)
	elif y3 <= -1.55e-270:
		tmp = t_1
	elif y3 <= 3e-224:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y3 <= 64000000000000.0:
		tmp = t_1
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y3 <= -2.25e+153)
		tmp = Float64(Float64(z * Float64(y0 * y3)) * Float64(0.0 - c));
	elseif (y3 <= -1.55e-270)
		tmp = t_1;
	elseif (y3 <= 3e-224)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 64000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y3 <= -2.25e+153)
		tmp = (z * (y0 * y3)) * (0.0 - c);
	elseif (y3 <= -1.55e-270)
		tmp = t_1;
	elseif (y3 <= 3e-224)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y3 <= 64000000000000.0)
		tmp = t_1;
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.25e+153], N[(N[(z * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.55e-270], t$95$1, If[LessEqual[y3, 3e-224], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 64000000000000.0], t$95$1, N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -2.25e153

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 35.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 43.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{t} \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 43.6%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y4 \cdot y2\right)\right)} \]

   12. Taylor expanded in y2 around 0

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \left(\left(y0 \cdot y3\right) \cdot \color{blue}{z}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y0 \cdot y3\right), \color{blue}{z}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y0\right), z\right)\right)\right) \]

       8. *-lowering-*.f64 43.2%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y0\right), z\right)\right)\right) \]

   14. Simplified 43.2%

       \[\leadsto \color{blue}{0 - c \cdot \left(\left(y3 \cdot y0\right) \cdot z\right)} \]

   if -2.25e153 < y3 < -1.55e-270 or 2.99999999999999982e-224 < y3 < 6.4e13

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.3%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -1.55e-270 < y3 < 2.99999999999999982e-224

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 42.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 6.4e13 < y3

   1. Initial program 18.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y0, \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(\color{blue}{y3} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 44.3%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.25 \cdot 10^{+153}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y3 \leq -1.55 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 3 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 64000000000000:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -3.7 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -8.6 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y3 \leq 5.7 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* z (* y0 y3)) (- 0.0 c)))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= y3 -3.7e+153)
     t_1
     (if (<= y3 -8.6e-272)
       t_2
       (if (<= y3 5.7e-224)
         (* b (* a (- (* x y) (* z t))))
         (if (<= y3 1e+67) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * (y0 * y3)) * (0.0 - c);
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -3.7e+153) {
		tmp = t_1;
	} else if (y3 <= -8.6e-272) {
		tmp = t_2;
	} else if (y3 <= 5.7e-224) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 1e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (y0 * y3)) * (0.0d0 - c)
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (y3 <= (-3.7d+153)) then
        tmp = t_1
    else if (y3 <= (-8.6d-272)) then
        tmp = t_2
    else if (y3 <= 5.7d-224) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y3 <= 1d+67) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * (y0 * y3)) * (0.0 - c);
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y3 <= -3.7e+153) {
		tmp = t_1;
	} else if (y3 <= -8.6e-272) {
		tmp = t_2;
	} else if (y3 <= 5.7e-224) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y3 <= 1e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * (y0 * y3)) * (0.0 - c)
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if y3 <= -3.7e+153:
		tmp = t_1
	elif y3 <= -8.6e-272:
		tmp = t_2
	elif y3 <= 5.7e-224:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y3 <= 1e+67:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * Float64(y0 * y3)) * Float64(0.0 - c))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y3 <= -3.7e+153)
		tmp = t_1;
	elseif (y3 <= -8.6e-272)
		tmp = t_2;
	elseif (y3 <= 5.7e-224)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 1e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * (y0 * y3)) * (0.0 - c);
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y3 <= -3.7e+153)
		tmp = t_1;
	elseif (y3 <= -8.6e-272)
		tmp = t_2;
	elseif (y3 <= 5.7e-224)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y3 <= 1e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3.7e+153], t$95$1, If[LessEqual[y3, -8.6e-272], t$95$2, If[LessEqual[y3, 5.7e-224], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1e+67], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -3.7000000000000002e153 or 9.99999999999999983e66 < y3

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 45.4%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 45.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{t} \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 46.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 46.9%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y4 \cdot y2\right)\right)} \]

   12. Taylor expanded in y2 around 0

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \left(\left(y0 \cdot y3\right) \cdot \color{blue}{z}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y0 \cdot y3\right), \color{blue}{z}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y0\right), z\right)\right)\right) \]

       8. *-lowering-*.f64 45.9%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y0\right), z\right)\right)\right) \]

   14. Simplified 45.9%

       \[\leadsto \color{blue}{0 - c \cdot \left(\left(y3 \cdot y0\right) \cdot z\right)} \]

   if -3.7000000000000002e153 < y3 < -8.5999999999999995e-272 or 5.6999999999999998e-224 < y3 < 9.99999999999999983e66

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -8.5999999999999995e-272 < y3 < 5.6999999999999998e-224

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 42.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.7 \cdot 10^{+153}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y3 \leq -8.6 \cdot 10^{-272}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 5.7 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+67}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -7.6 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-21}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{+247}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(0 - c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (* y3 y4)))))
   (if (<= y4 -7.6e+235)
     t_1
     (if (<= y4 -9e-21)
       (* c (* y2 (- 0.0 (* t y4))))
       (if (<= y4 8.2e-54)
         (* (* i j) (- 0.0 (* t y5)))
         (if (<= y4 4.4e+247) (* (* t (* y2 y4)) (- 0.0 c)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -7.6e+235) {
		tmp = t_1;
	} else if (y4 <= -9e-21) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y4 <= 8.2e-54) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (y4 <= 4.4e+247) {
		tmp = (t * (y2 * y4)) * (0.0 - c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y * (y3 * y4))
    if (y4 <= (-7.6d+235)) then
        tmp = t_1
    else if (y4 <= (-9d-21)) then
        tmp = c * (y2 * (0.0d0 - (t * y4)))
    else if (y4 <= 8.2d-54) then
        tmp = (i * j) * (0.0d0 - (t * y5))
    else if (y4 <= 4.4d+247) then
        tmp = (t * (y2 * y4)) * (0.0d0 - c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * (y3 * y4));
	double tmp;
	if (y4 <= -7.6e+235) {
		tmp = t_1;
	} else if (y4 <= -9e-21) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y4 <= 8.2e-54) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (y4 <= 4.4e+247) {
		tmp = (t * (y2 * y4)) * (0.0 - c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y * (y3 * y4))
	tmp = 0
	if y4 <= -7.6e+235:
		tmp = t_1
	elif y4 <= -9e-21:
		tmp = c * (y2 * (0.0 - (t * y4)))
	elif y4 <= 8.2e-54:
		tmp = (i * j) * (0.0 - (t * y5))
	elif y4 <= 4.4e+247:
		tmp = (t * (y2 * y4)) * (0.0 - c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(y3 * y4)))
	tmp = 0.0
	if (y4 <= -7.6e+235)
		tmp = t_1;
	elseif (y4 <= -9e-21)
		tmp = Float64(c * Float64(y2 * Float64(0.0 - Float64(t * y4))));
	elseif (y4 <= 8.2e-54)
		tmp = Float64(Float64(i * j) * Float64(0.0 - Float64(t * y5)));
	elseif (y4 <= 4.4e+247)
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(0.0 - c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y * (y3 * y4));
	tmp = 0.0;
	if (y4 <= -7.6e+235)
		tmp = t_1;
	elseif (y4 <= -9e-21)
		tmp = c * (y2 * (0.0 - (t * y4)));
	elseif (y4 <= 8.2e-54)
		tmp = (i * j) * (0.0 - (t * y5));
	elseif (y4 <= 4.4e+247)
		tmp = (t * (y2 * y4)) * (0.0 - c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -7.6e+235], t$95$1, If[LessEqual[y4, -9e-21], N[(c * N[(y2 * N[(0.0 - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 8.2e-54], N[(N[(i * j), $MachinePrecision] * N[(0.0 - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.4e+247], N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -7.5999999999999995e235 or 4.40000000000000022e247 < y4

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 39.4%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 49.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 49.4%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]

   if -7.5999999999999995e235 < y4 < -8.99999999999999936e-21

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 48.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 48.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 34.6%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 34.6%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y4\right) \cdot y2\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\mathsf{neg}\left(\color{blue}{y2}\right)\right)\right)\right) \]

       6. neg-lowering-neg.f64 42.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{neg.f64}\left(y2\right)\right)\right) \]

   13. Applied egg-rr 42.4%

       \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)} \]

   if -8.99999999999999936e-21 < y4 < 8.2000000000000001e-54

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 28.2%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 28.2%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \color{blue}{\left(t \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(y5 \cdot t\right)\right)\right) \]

       2. *-lowering-*.f64 22.7%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{*.f64}\left(y5, t\right)\right)\right) \]

   11. Simplified 22.7%

       \[\leadsto -\left(i \cdot j\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   if 8.2000000000000001e-54 < y4 < 4.40000000000000022e247

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 47.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 38.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 38.4%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, \left(y4 \cdot y2\right)\right)\right)\right) \]

       4. *-lowering-*.f64 38.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

   13. Applied egg-rr 38.4%

       \[\leadsto c \cdot \color{blue}{\left(-t \cdot \left(y4 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -7.6 \cdot 10^{+235}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-21}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{+247}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(0 - c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+172}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* z k) (- (* b y0) (* i y1)))))
   (if (<= z -7.8e+96)
     t_1
     (if (<= z 1.7e-280)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= z 1.45e+172) (* (* c y2) (- (* x y0) (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * k) * ((b * y0) - (i * y1));
	double tmp;
	if (z <= -7.8e+96) {
		tmp = t_1;
	} else if (z <= 1.7e-280) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (z <= 1.45e+172) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * k) * ((b * y0) - (i * y1))
    if (z <= (-7.8d+96)) then
        tmp = t_1
    else if (z <= 1.7d-280) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (z <= 1.45d+172) then
        tmp = (c * y2) * ((x * y0) - (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * k) * ((b * y0) - (i * y1));
	double tmp;
	if (z <= -7.8e+96) {
		tmp = t_1;
	} else if (z <= 1.7e-280) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (z <= 1.45e+172) {
		tmp = (c * y2) * ((x * y0) - (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * k) * ((b * y0) - (i * y1))
	tmp = 0
	if z <= -7.8e+96:
		tmp = t_1
	elif z <= 1.7e-280:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif z <= 1.45e+172:
		tmp = (c * y2) * ((x * y0) - (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * k) * Float64(Float64(b * y0) - Float64(i * y1)))
	tmp = 0.0
	if (z <= -7.8e+96)
		tmp = t_1;
	elseif (z <= 1.7e-280)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (z <= 1.45e+172)
		tmp = Float64(Float64(c * y2) * Float64(Float64(x * y0) - Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * k) * ((b * y0) - (i * y1));
	tmp = 0.0;
	if (z <= -7.8e+96)
		tmp = t_1;
	elseif (z <= 1.7e-280)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (z <= 1.45e+172)
		tmp = (c * y2) * ((x * y0) - (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * k), $MachinePrecision] * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+96], t$95$1, If[LessEqual[z, 1.7e-280], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+172], N[(N[(c * y2), $MachinePrecision] * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e96 or 1.45e172 < z

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot z\right) \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \left(\color{blue}{\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(t \cdot \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(\color{blue}{k} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(a \cdot b - c \cdot i\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(a \cdot b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(c \cdot i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \left(y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \left(c \cdot y0 - a \cdot y1\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \left(k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, z\right), \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(c, i\right)\right)\right), \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right)\right), \mathsf{*.f64}\left(k, \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right)\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in k around -inf

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(k \cdot z\right) \cdot \color{blue}{\left(b \cdot y0 - i \cdot y1\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(k \cdot z\right), \color{blue}{\left(b \cdot y0 - i \cdot y1\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, z\right), \left(\color{blue}{b \cdot y0} - i \cdot y1\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{\_.f64}\left(\left(b \cdot y0\right), \color{blue}{\left(i \cdot y1\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \left(\color{blue}{i} \cdot y1\right)\right)\right) \]

      6. *-lowering-*.f64 54.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, z\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y0\right), \mathsf{*.f64}\left(i, \color{blue}{y1}\right)\right)\right) \]

   8. Simplified 54.2%

      \[\leadsto \color{blue}{\left(k \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)} \]

   if -7.8e96 < z < 1.6999999999999999e-280

   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 j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 43.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 43.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 43.0%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   if 1.6999999999999999e-280 < z < 1.45e172

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{x \cdot y0} - t \cdot y4\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y0\right), \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \left(\color{blue}{t} \cdot y4\right)\right)\right) \]

      6. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \mathsf{*.f64}\left(t, \color{blue}{y4}\right)\right)\right) \]

   8. Simplified 43.9%

      \[\leadsto \color{blue}{\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+96}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+172}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y0 (- (* y3 y5) (* x b))))))
   (if (<= y0 -1.05e+46)
     t_1
     (if (<= y0 1.4e-63)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= y0 2.2e+102) (* j (* x (- (* i y1) (* b 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 = j * (y0 * ((y3 * y5) - (x * b)));
	double tmp;
	if (y0 <= -1.05e+46) {
		tmp = t_1;
	} else if (y0 <= 1.4e-63) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y0 <= 2.2e+102) {
		tmp = j * (x * ((i * y1) - (b * 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 = j * (y0 * ((y3 * y5) - (x * b)))
    if (y0 <= (-1.05d+46)) then
        tmp = t_1
    else if (y0 <= 1.4d-63) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y0 <= 2.2d+102) then
        tmp = j * (x * ((i * y1) - (b * 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 = j * (y0 * ((y3 * y5) - (x * b)));
	double tmp;
	if (y0 <= -1.05e+46) {
		tmp = t_1;
	} else if (y0 <= 1.4e-63) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y0 <= 2.2e+102) {
		tmp = j * (x * ((i * y1) - (b * 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 = j * (y0 * ((y3 * y5) - (x * b)))
	tmp = 0
	if y0 <= -1.05e+46:
		tmp = t_1
	elif y0 <= 1.4e-63:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y0 <= 2.2e+102:
		tmp = j * (x * ((i * y1) - (b * 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(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))))
	tmp = 0.0
	if (y0 <= -1.05e+46)
		tmp = t_1;
	elseif (y0 <= 1.4e-63)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y0 <= 2.2e+102)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * 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 = j * (y0 * ((y3 * y5) - (x * b)));
	tmp = 0.0;
	if (y0 <= -1.05e+46)
		tmp = t_1;
	elseif (y0 <= 1.4e-63)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y0 <= 2.2e+102)
		tmp = j * (x * ((i * y1) - (b * 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[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.05e+46], t$95$1, If[LessEqual[y0, 1.4e-63], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e+102], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -1.05e46 or 2.20000000000000007e102 < y0

   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 j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in y0 around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(y3 \cdot y5\right), \color{blue}{\left(b \cdot x\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \left(\color{blue}{b} \cdot x\right)\right)\right)\right) \]

      4. *-lowering-*.f64 48.9%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y3, y5\right), \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right)\right) \]

   8. Simplified 48.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   if -1.05e46 < y0 < 1.4000000000000001e-63

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 37.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot z\right), \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \left(\color{blue}{y2} \cdot y4\right)\right)\right)\right) \]

      4. *-lowering-*.f64 38.0%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, z\right), \mathsf{*.f64}\left(y2, \color{blue}{y4}\right)\right)\right)\right) \]

   8. Simplified 38.0%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 1.4000000000000001e-63 < y0 < 2.20000000000000007e102

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(i \cdot y1\right), \color{blue}{\left(b \cdot y0\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \left(\color{blue}{b} \cdot y0\right)\right)\right)\right) \]

      4. *-lowering-*.f64 50.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 50.0%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \mathbf{if}\;y3 \leq -3.4 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-145}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* z (* y0 y3)) (- 0.0 c))))
   (if (<= y3 -3.4e+146)
     t_1
     (if (<= y3 -9.2e-145)
       (* c (* y2 (- 0.0 (* t y4))))
       (if (<= y3 2.35e+70) (* 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 = (z * (y0 * y3)) * (0.0 - c);
	double tmp;
	if (y3 <= -3.4e+146) {
		tmp = t_1;
	} else if (y3 <= -9.2e-145) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y3 <= 2.35e+70) {
		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 = (z * (y0 * y3)) * (0.0d0 - c)
    if (y3 <= (-3.4d+146)) then
        tmp = t_1
    else if (y3 <= (-9.2d-145)) then
        tmp = c * (y2 * (0.0d0 - (t * y4)))
    else if (y3 <= 2.35d+70) 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 = (z * (y0 * y3)) * (0.0 - c);
	double tmp;
	if (y3 <= -3.4e+146) {
		tmp = t_1;
	} else if (y3 <= -9.2e-145) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else if (y3 <= 2.35e+70) {
		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 = (z * (y0 * y3)) * (0.0 - c)
	tmp = 0
	if y3 <= -3.4e+146:
		tmp = t_1
	elif y3 <= -9.2e-145:
		tmp = c * (y2 * (0.0 - (t * y4)))
	elif y3 <= 2.35e+70:
		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(Float64(z * Float64(y0 * y3)) * Float64(0.0 - c))
	tmp = 0.0
	if (y3 <= -3.4e+146)
		tmp = t_1;
	elseif (y3 <= -9.2e-145)
		tmp = Float64(c * Float64(y2 * Float64(0.0 - Float64(t * y4))));
	elseif (y3 <= 2.35e+70)
		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 = (z * (y0 * y3)) * (0.0 - c);
	tmp = 0.0;
	if (y3 <= -3.4e+146)
		tmp = t_1;
	elseif (y3 <= -9.2e-145)
		tmp = c * (y2 * (0.0 - (t * y4)));
	elseif (y3 <= 2.35e+70)
		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[(N[(z * N[(y0 * y3), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3.4e+146], t$95$1, If[LessEqual[y3, -9.2e-145], N[(c * N[(y2 * N[(0.0 - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.35e+70], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -3.39999999999999991e146 or 2.3499999999999999e70 < y3

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 45.4%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 45.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{t} \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       9. *-lowering-*.f64 47.0%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - t \cdot \left(y4 \cdot y2\right)\right)} \]

   12. Taylor expanded in y2 around 0

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \left(\left(y0 \cdot y3\right) \cdot \color{blue}{z}\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y0 \cdot y3\right), \color{blue}{z}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y0\right), z\right)\right)\right) \]

       8. *-lowering-*.f64 45.9%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y0\right), z\right)\right)\right) \]

   14. Simplified 45.9%

       \[\leadsto \color{blue}{0 - c \cdot \left(\left(y3 \cdot y0\right) \cdot z\right)} \]

   if -3.39999999999999991e146 < y3 < -9.20000000000000028e-145

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 40.4%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 40.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 28.0%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 28.0%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y4\right) \cdot y2\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\mathsf{neg}\left(\color{blue}{y2}\right)\right)\right)\right) \]

       6. neg-lowering-neg.f64 29.7%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{neg.f64}\left(y2\right)\right)\right) \]

   13. Applied egg-rr 29.7%

       \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)} \]

   if -9.20000000000000028e-145 < y3 < 2.3499999999999999e70

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 30.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 30.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.4 \cdot 10^{+146}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-145}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y0 \cdot y3\right)\right) \cdot \left(0 - c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.9% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-260}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(0 - t \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(0 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -1.75e+145)
   (* a (* y1 (* z y3)))
   (if (<= z -1.3e-260)
     (* (* i j) (- 0.0 (* t y5)))
     (if (<= z 1.35e+156)
       (* (* c y2) (- 0.0 (* t y4)))
       (* c (* y0 (- 0.0 (* 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) {
	double tmp;
	if (z <= -1.75e+145) {
		tmp = a * (y1 * (z * y3));
	} else if (z <= -1.3e-260) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (z <= 1.35e+156) {
		tmp = (c * y2) * (0.0 - (t * y4));
	} else {
		tmp = c * (y0 * (0.0 - (z * 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 (z <= (-1.75d+145)) then
        tmp = a * (y1 * (z * y3))
    else if (z <= (-1.3d-260)) then
        tmp = (i * j) * (0.0d0 - (t * y5))
    else if (z <= 1.35d+156) then
        tmp = (c * y2) * (0.0d0 - (t * y4))
    else
        tmp = c * (y0 * (0.0d0 - (z * 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 (z <= -1.75e+145) {
		tmp = a * (y1 * (z * y3));
	} else if (z <= -1.3e-260) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (z <= 1.35e+156) {
		tmp = (c * y2) * (0.0 - (t * y4));
	} else {
		tmp = c * (y0 * (0.0 - (z * 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 z <= -1.75e+145:
		tmp = a * (y1 * (z * y3))
	elif z <= -1.3e-260:
		tmp = (i * j) * (0.0 - (t * y5))
	elif z <= 1.35e+156:
		tmp = (c * y2) * (0.0 - (t * y4))
	else:
		tmp = c * (y0 * (0.0 - (z * 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 (z <= -1.75e+145)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (z <= -1.3e-260)
		tmp = Float64(Float64(i * j) * Float64(0.0 - Float64(t * y5)));
	elseif (z <= 1.35e+156)
		tmp = Float64(Float64(c * y2) * Float64(0.0 - Float64(t * y4)));
	else
		tmp = Float64(c * Float64(y0 * Float64(0.0 - Float64(z * 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 (z <= -1.75e+145)
		tmp = a * (y1 * (z * y3));
	elseif (z <= -1.3e-260)
		tmp = (i * j) * (0.0 - (t * y5));
	elseif (z <= 1.35e+156)
		tmp = (c * y2) * (0.0 - (t * y4));
	else
		tmp = c * (y0 * (0.0 - (z * 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[z, -1.75e+145], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-260], N[(N[(i * j), $MachinePrecision] * N[(0.0 - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+156], N[(N[(c * y2), $MachinePrecision] * N[(0.0 - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(0.0 - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7500000000000001e145

   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 y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y3\right) \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a 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. associate-*r* N/A

         \[\leadsto \left(a \cdot y3\right) \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{y1 \cdot z} - y \cdot y5\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right) \]

      6. *-lowering-*.f64 28.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right) \]

   8. Simplified 28.6%

      \[\leadsto \color{blue}{\left(a \cdot y3\right) \cdot \left(y1 \cdot z - y \cdot y5\right)} \]

   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 32.4%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 32.4%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.7500000000000001e145 < z < -1.29999999999999997e-260

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \color{blue}{\left(t \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(y5 \cdot t\right)\right)\right) \]

       2. *-lowering-*.f64 29.8%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{*.f64}\left(y5, t\right)\right)\right) \]

   11. Simplified 29.8%

       \[\leadsto -\left(i \cdot j\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   if -1.29999999999999997e-260 < z < 1.35e156

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{x \cdot y0} - t \cdot y4\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y0\right), \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \left(\color{blue}{t} \cdot y4\right)\right)\right) \]

      6. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \mathsf{*.f64}\left(t, \color{blue}{y4}\right)\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \color{blue}{\left(-1 \cdot \left(t \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\mathsf{neg}\left(t \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(t \cdot \left(-1 \cdot \color{blue}{y4}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(y4\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(t, \left(0 - \color{blue}{y4}\right)\right)\right) \]

       7. --lowering--.f64 35.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(0, \color{blue}{y4}\right)\right)\right) \]

   11. Simplified 35.3%

       \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(t \cdot \left(0 - y4\right)\right)} \]

   if 1.35e156 < z

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 31.9%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 31.9%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{y0 \cdot \left(y3 \cdot z\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 35.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   11. Simplified 35.3%

       \[\leadsto \color{blue}{c \cdot \left(0 - y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-260}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(0 - t \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(0 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-259}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+152}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(0 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.7e+143)
   (* a (* y1 (* z y3)))
   (if (<= z -1.08e-259)
     (* (* i j) (- 0.0 (* t y5)))
     (if (<= z 1.7e+152)
       (* c (* y2 (- 0.0 (* t y4))))
       (* c (* y0 (- 0.0 (* 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) {
	double tmp;
	if (z <= -2.7e+143) {
		tmp = a * (y1 * (z * y3));
	} else if (z <= -1.08e-259) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (z <= 1.7e+152) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else {
		tmp = c * (y0 * (0.0 - (z * 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 (z <= (-2.7d+143)) then
        tmp = a * (y1 * (z * y3))
    else if (z <= (-1.08d-259)) then
        tmp = (i * j) * (0.0d0 - (t * y5))
    else if (z <= 1.7d+152) then
        tmp = c * (y2 * (0.0d0 - (t * y4)))
    else
        tmp = c * (y0 * (0.0d0 - (z * 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 (z <= -2.7e+143) {
		tmp = a * (y1 * (z * y3));
	} else if (z <= -1.08e-259) {
		tmp = (i * j) * (0.0 - (t * y5));
	} else if (z <= 1.7e+152) {
		tmp = c * (y2 * (0.0 - (t * y4)));
	} else {
		tmp = c * (y0 * (0.0 - (z * 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 z <= -2.7e+143:
		tmp = a * (y1 * (z * y3))
	elif z <= -1.08e-259:
		tmp = (i * j) * (0.0 - (t * y5))
	elif z <= 1.7e+152:
		tmp = c * (y2 * (0.0 - (t * y4)))
	else:
		tmp = c * (y0 * (0.0 - (z * 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 (z <= -2.7e+143)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	elseif (z <= -1.08e-259)
		tmp = Float64(Float64(i * j) * Float64(0.0 - Float64(t * y5)));
	elseif (z <= 1.7e+152)
		tmp = Float64(c * Float64(y2 * Float64(0.0 - Float64(t * y4))));
	else
		tmp = Float64(c * Float64(y0 * Float64(0.0 - Float64(z * 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 (z <= -2.7e+143)
		tmp = a * (y1 * (z * y3));
	elseif (z <= -1.08e-259)
		tmp = (i * j) * (0.0 - (t * y5));
	elseif (z <= 1.7e+152)
		tmp = c * (y2 * (0.0 - (t * y4)));
	else
		tmp = c * (y0 * (0.0 - (z * 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[z, -2.7e+143], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-259], N[(N[(i * j), $MachinePrecision] * N[(0.0 - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+152], N[(c * N[(y2 * N[(0.0 - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(0.0 - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7000000000000002e143

   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 y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y3\right) \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a 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. associate-*r* N/A

         \[\leadsto \left(a \cdot y3\right) \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{y1 \cdot z} - y \cdot y5\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right) \]

      6. *-lowering-*.f64 28.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right) \]

   8. Simplified 28.6%

      \[\leadsto \color{blue}{\left(a \cdot y3\right) \cdot \left(y1 \cdot z - y \cdot y5\right)} \]

   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 32.4%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 32.4%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -2.7000000000000002e143 < z < -1.08000000000000002e-259

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \color{blue}{\left(t \cdot y5\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(y5 \cdot t\right)\right)\right) \]

       2. *-lowering-*.f64 29.8%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{*.f64}\left(y5, t\right)\right)\right) \]

   11. Simplified 29.8%

       \[\leadsto -\left(i \cdot j\right) \cdot \color{blue}{\left(y5 \cdot t\right)} \]

   if -1.08000000000000002e-259 < z < 1.7000000000000001e152

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 44.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 43.5%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 43.5%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 29.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 29.5%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y4\right) \cdot y2\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(t \cdot y4\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(\mathsf{neg}\left(y2\right)\right)}\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\mathsf{neg}\left(\color{blue}{y2}\right)\right)\right)\right) \]

       6. neg-lowering-neg.f64 33.4%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{neg.f64}\left(y2\right)\right)\right) \]

   13. Applied egg-rr 33.4%

       \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)} \]

   if 1.7000000000000001e152 < z

   1. Initial program 48.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 31.9%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 31.9%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(y0 \cdot \left(y3 \cdot z\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{y0 \cdot \left(y3 \cdot z\right)}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(y0 \cdot \left(y3 \cdot z\right)\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \color{blue}{\left(y3 \cdot z\right)}\right)\right)\right) \]

       9. *-lowering-*.f64 35.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y0, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right)\right) \]

   11. Simplified 35.3%

       \[\leadsto \color{blue}{c \cdot \left(0 - y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-259}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(0 - t \cdot y5\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+152}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(0 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+169}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.65e+169)
   (* (* c y2) (* x y0))
   (if (<= x -2.4e+82)
     (* i (* j (* x y1)))
     (if (<= x 4.2e+72) (* c (* y (* y3 y4))) (* y (* a (* x b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.65e+169) {
		tmp = (c * y2) * (x * y0);
	} else if (x <= -2.4e+82) {
		tmp = i * (j * (x * y1));
	} else if (x <= 4.2e+72) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y * (a * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.65d+169)) then
        tmp = (c * y2) * (x * y0)
    else if (x <= (-2.4d+82)) then
        tmp = i * (j * (x * y1))
    else if (x <= 4.2d+72) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = y * (a * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.65e+169) {
		tmp = (c * y2) * (x * y0);
	} else if (x <= -2.4e+82) {
		tmp = i * (j * (x * y1));
	} else if (x <= 4.2e+72) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y * (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.65e+169:
		tmp = (c * y2) * (x * y0)
	elif x <= -2.4e+82:
		tmp = i * (j * (x * y1))
	elif x <= 4.2e+72:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = y * (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.65e+169)
		tmp = Float64(Float64(c * y2) * Float64(x * y0));
	elseif (x <= -2.4e+82)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 4.2e+72)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(y * Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.65e+169)
		tmp = (c * y2) * (x * y0);
	elseif (x <= -2.4e+82)
		tmp = i * (j * (x * y1));
	elseif (x <= 4.2e+72)
		tmp = c * (y * (y3 * y4));
	else
		tmp = y * (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.65e+169], N[(N[(c * y2), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+82], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+72], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6499999999999998e169

   1. Initial program 4.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{x \cdot y0} - t \cdot y4\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y0\right), \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \left(\color{blue}{t} \cdot y4\right)\right)\right) \]

      6. *-lowering-*.f64 59.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \mathsf{*.f64}\left(t, \color{blue}{y4}\right)\right)\right) \]

   8. Simplified 59.3%

      \[\leadsto \color{blue}{\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \color{blue}{\left(x \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(y0 \cdot \color{blue}{x}\right)\right) \]

       2. *-lowering-*.f64 59.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(y0, \color{blue}{x}\right)\right) \]

   11. Simplified 59.6%

       \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(y0 \cdot x\right)} \]

   if -1.6499999999999998e169 < x < -2.39999999999999998e82

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t 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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \left(y1 \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -2.39999999999999998e82 < x < 4.2000000000000003e72

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 33.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 21.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]

   if 4.2000000000000003e72 < x

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 24.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 24.2%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       3. *-lowering-*.f64 20.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 20.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \left(\left(b \cdot x\right) \cdot \color{blue}{y}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(b \cdot x\right)\right) \cdot \color{blue}{y} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(b \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot x\right)\right), y\right) \]

       5. *-lowering-*.f64 31.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, x\right)\right), y\right) \]

   13. Applied egg-rr 31.8%

       \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot x\right)\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+169}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.75e+172)
   (* c (* x (* y0 y2)))
   (if (<= x -3.1e+82)
     (* i (* j (* x y1)))
     (if (<= x 2.7e+70) (* c (* y (* y3 y4))) (* y (* a (* x b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.75e+172) {
		tmp = c * (x * (y0 * y2));
	} else if (x <= -3.1e+82) {
		tmp = i * (j * (x * y1));
	} else if (x <= 2.7e+70) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y * (a * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-2.75d+172)) then
        tmp = c * (x * (y0 * y2))
    else if (x <= (-3.1d+82)) then
        tmp = i * (j * (x * y1))
    else if (x <= 2.7d+70) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = y * (a * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -2.75e+172) {
		tmp = c * (x * (y0 * y2));
	} else if (x <= -3.1e+82) {
		tmp = i * (j * (x * y1));
	} else if (x <= 2.7e+70) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y * (a * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.75e+172:
		tmp = c * (x * (y0 * y2))
	elif x <= -3.1e+82:
		tmp = i * (j * (x * y1))
	elif x <= 2.7e+70:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = y * (a * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.75e+172)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (x <= -3.1e+82)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 2.7e+70)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(y * Float64(a * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -2.75e+172)
		tmp = c * (x * (y0 * y2));
	elseif (x <= -3.1e+82)
		tmp = i * (j * (x * y1));
	elseif (x <= 2.7e+70)
		tmp = c * (y * (y3 * y4));
	else
		tmp = y * (a * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -2.75e+172], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e+82], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+70], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.75e172

   1. Initial program 4.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 54.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{\left(y0 \cdot y2\right)}\right)\right) \]

       3. *-lowering-*.f64 55.3%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 55.3%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.75e172 < x < -3.10000000000000032e82

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t 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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \left(y1 \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.10000000000000032e82 < x < 2.7e70

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 33.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 21.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]

   if 2.7e70 < x

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 24.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 24.2%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       3. *-lowering-*.f64 20.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 20.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \left(\left(b \cdot x\right) \cdot \color{blue}{y}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(b \cdot x\right)\right) \cdot \color{blue}{y} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(b \cdot x\right)\right), \color{blue}{y}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot x\right)\right), y\right) \]

       5. *-lowering-*.f64 31.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, x\right)\right), y\right) \]

   13. Applied egg-rr 31.8%

       \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot x\right)\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+172}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= x -9.6e+173)
     t_1
     (if (<= x -1.9e+86)
       (* i (* j (* x y1)))
       (if (<= x 4.4e+71) (* c (* y (* y3 y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -9.6e+173) {
		tmp = t_1;
	} else if (x <= -1.9e+86) {
		tmp = i * (j * (x * y1));
	} else if (x <= 4.4e+71) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (x <= (-9.6d+173)) then
        tmp = t_1
    else if (x <= (-1.9d+86)) then
        tmp = i * (j * (x * y1))
    else if (x <= 4.4d+71) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -9.6e+173) {
		tmp = t_1;
	} else if (x <= -1.9e+86) {
		tmp = i * (j * (x * y1));
	} else if (x <= 4.4e+71) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if x <= -9.6e+173:
		tmp = t_1
	elif x <= -1.9e+86:
		tmp = i * (j * (x * y1))
	elif x <= 4.4e+71:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (x <= -9.6e+173)
		tmp = t_1;
	elseif (x <= -1.9e+86)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= 4.4e+71)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (x <= -9.6e+173)
		tmp = t_1;
	elseif (x <= -1.9e+86)
		tmp = i * (j * (x * y1));
	elseif (x <= 4.4e+71)
		tmp = c * (y * (y3 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+173], t$95$1, If[LessEqual[x, -1.9e+86], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+71], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999997e173 or 4.39999999999999989e71 < x

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 35.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 35.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{\left(y0 \cdot y2\right)}\right)\right) \]

       3. *-lowering-*.f64 35.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 35.9%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -9.5999999999999997e173 < x < -1.89999999999999989e86

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t 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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \left(y1 \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 50.6%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.89999999999999989e86 < x < 4.39999999999999989e71

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 33.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 21.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 19.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -5.6 \cdot 10^{-158}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{+34}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(0 - t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -5.6e-158)
   (* (* t (* y2 y4)) (- 0.0 c))
   (if (<= y5 2.05e+34) (* (* c y2) (* x y0)) (* i (* j (- 0.0 (* t 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 (y5 <= -5.6e-158) {
		tmp = (t * (y2 * y4)) * (0.0 - c);
	} else if (y5 <= 2.05e+34) {
		tmp = (c * y2) * (x * y0);
	} else {
		tmp = i * (j * (0.0 - (t * 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 (y5 <= (-5.6d-158)) then
        tmp = (t * (y2 * y4)) * (0.0d0 - c)
    else if (y5 <= 2.05d+34) then
        tmp = (c * y2) * (x * y0)
    else
        tmp = i * (j * (0.0d0 - (t * 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 (y5 <= -5.6e-158) {
		tmp = (t * (y2 * y4)) * (0.0 - c);
	} else if (y5 <= 2.05e+34) {
		tmp = (c * y2) * (x * y0);
	} else {
		tmp = i * (j * (0.0 - (t * 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 y5 <= -5.6e-158:
		tmp = (t * (y2 * y4)) * (0.0 - c)
	elif y5 <= 2.05e+34:
		tmp = (c * y2) * (x * y0)
	else:
		tmp = i * (j * (0.0 - (t * 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 (y5 <= -5.6e-158)
		tmp = Float64(Float64(t * Float64(y2 * y4)) * Float64(0.0 - c));
	elseif (y5 <= 2.05e+34)
		tmp = Float64(Float64(c * y2) * Float64(x * y0));
	else
		tmp = Float64(i * Float64(j * Float64(0.0 - Float64(t * 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 (y5 <= -5.6e-158)
		tmp = (t * (y2 * y4)) * (0.0 - c);
	elseif (y5 <= 2.05e+34)
		tmp = (c * y2) * (x * y0);
	else
		tmp = i * (j * (0.0 - (t * 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[y5, -5.6e-158], N[(N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(0.0 - c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.05e+34], N[(N[(c * y2), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(0.0 - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -5.60000000000000004e-158

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 32.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       4. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(0 - \color{blue}{t \cdot \left(y2 \cdot y4\right)}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(y2 \cdot y4\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \left(y4 \cdot \color{blue}{y2}\right)\right)\right)\right) \]

       8. *-lowering-*.f64 22.7%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, \color{blue}{y2}\right)\right)\right)\right) \]

   11. Simplified 22.7%

       \[\leadsto \color{blue}{c \cdot \left(0 - t \cdot \left(y4 \cdot y2\right)\right)} \]
   12. Step-by-step derivation

       1. sub0-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       2. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\left(t \cdot \left(y4 \cdot y2\right)\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, \left(y4 \cdot y2\right)\right)\right)\right) \]

       4. *-lowering-*.f64 22.7%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y4, y2\right)\right)\right)\right) \]

   13. Applied egg-rr 22.7%

       \[\leadsto c \cdot \color{blue}{\left(-t \cdot \left(y4 \cdot y2\right)\right)} \]

   if -5.60000000000000004e-158 < y5 < 2.0499999999999999e34

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(c \cdot y2\right), \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(\color{blue}{x \cdot y0} - t \cdot y4\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y0\right), \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \left(\color{blue}{t} \cdot y4\right)\right)\right) \]

      6. *-lowering-*.f64 29.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y0\right), \mathsf{*.f64}\left(t, \color{blue}{y4}\right)\right)\right) \]

   8. Simplified 29.6%

      \[\leadsto \color{blue}{\left(c \cdot y2\right) \cdot \left(x \cdot y0 - t \cdot y4\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \color{blue}{\left(x \cdot y0\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \left(y0 \cdot \color{blue}{x}\right)\right) \]

       2. *-lowering-*.f64 25.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(c, y2\right), \mathsf{*.f64}\left(y0, \color{blue}{x}\right)\right) \]

   11. Simplified 25.3%

       \[\leadsto \left(c \cdot y2\right) \cdot \color{blue}{\left(y0 \cdot x\right)} \]

   if 2.0499999999999999e34 < y5

   1. Initial program 17.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right), \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t \cdot \left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{t} \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(t \cdot \left(\color{blue}{b \cdot y4} - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right), \color{blue}{\left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot y4 - i \cdot y5\right)\right), \left(\color{blue}{x} \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(i \cdot y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, y5\right)\right)\right), \left(\left(b \cdot y0 - i \cdot y1\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(i \cdot \left(j \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(i \cdot j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \left(t \cdot y5 - x \cdot y1\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\left(t \cdot y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \left(x \cdot y1\right)\right)\right)\right) \]

      8. *-lowering-*.f64 37.6%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(i, j\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y5\right), \mathsf{*.f64}\left(x, y1\right)\right)\right)\right) \]

   8. Simplified 37.6%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot \left(t \cdot y5 - x \cdot y1\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{neg.f64}\left(\color{blue}{\left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(i, \left(j \cdot \left(t \cdot y5\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \left(t \cdot y5\right)\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \left(y5 \cdot t\right)\right)\right)\right) \]

       4. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y5, t\right)\right)\right)\right) \]

   11. Simplified 46.1%

       \[\leadsto -\color{blue}{i \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.6 \cdot 10^{-158}:\\ \;\;\;\;\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(0 - c\right)\\ \mathbf{elif}\;y5 \leq 2.05 \cdot 10^{+34}:\\ \;\;\;\;\left(c \cdot y2\right) \cdot \left(x \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(0 - t \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (* y0 y2)))))
   (if (<= x -1.15e+85) t_1 (if (<= x 7.8e+71) (* c (* y (* y3 y4))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -1.15e+85) {
		tmp = t_1;
	} else if (x <= 7.8e+71) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (x * (y0 * y2))
    if (x <= (-1.15d+85)) then
        tmp = t_1
    else if (x <= 7.8d+71) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * (y0 * y2));
	double tmp;
	if (x <= -1.15e+85) {
		tmp = t_1;
	} else if (x <= 7.8e+71) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * (y0 * y2))
	tmp = 0
	if x <= -1.15e+85:
		tmp = t_1
	elif x <= 7.8e+71:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(y0 * y2)))
	tmp = 0.0
	if (x <= -1.15e+85)
		tmp = t_1;
	elseif (x <= 7.8e+71)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * (y0 * y2));
	tmp = 0.0;
	if (x <= -1.15e+85)
		tmp = t_1;
	elseif (x <= 7.8e+71)
		tmp = c * (y * (y3 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+85], t$95$1, If[LessEqual[x, 7.8e+71], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e85 or 7.8000000000000002e71 < x

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{\left(y0 \cdot y2\right)}\right)\right) \]

       3. *-lowering-*.f64 32.9%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 32.9%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -1.1499999999999999e85 < x < 7.8000000000000002e71

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 33.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 33.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(y3 \cdot y4\right) \cdot \color{blue}{y}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(y3 \cdot y4\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y3, y4\right), y\right)\right) \]

   11. Simplified 21.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* z y3)))))
   (if (<= z -1.8e+19) t_1 (if (<= z 1.95e+157) (* c (* x (* y0 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 = a * (y1 * (z * y3));
	double tmp;
	if (z <= -1.8e+19) {
		tmp = t_1;
	} else if (z <= 1.95e+157) {
		tmp = c * (x * (y0 * 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 = a * (y1 * (z * y3))
    if (z <= (-1.8d+19)) then
        tmp = t_1
    else if (z <= 1.95d+157) then
        tmp = c * (x * (y0 * 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 = a * (y1 * (z * y3));
	double tmp;
	if (z <= -1.8e+19) {
		tmp = t_1;
	} else if (z <= 1.95e+157) {
		tmp = c * (x * (y0 * 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 = a * (y1 * (z * y3))
	tmp = 0
	if z <= -1.8e+19:
		tmp = t_1
	elif z <= 1.95e+157:
		tmp = c * (x * (y0 * 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(a * Float64(y1 * Float64(z * y3)))
	tmp = 0.0
	if (z <= -1.8e+19)
		tmp = t_1;
	elseif (z <= 1.95e+157)
		tmp = Float64(c * Float64(x * Float64(y0 * 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 = a * (y1 * (z * y3));
	tmp = 0.0;
	if (z <= -1.8e+19)
		tmp = t_1;
	elseif (z <= 1.95e+157)
		tmp = c * (x * (y0 * 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[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+19], t$95$1, If[LessEqual[z, 1.95e+157], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e19 or 1.94999999999999985e157 < z

   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 y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y3\right) \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a 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. associate-*r* N/A

         \[\leadsto \left(a \cdot y3\right) \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{y1 \cdot z} - y \cdot y5\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right) \]

      6. *-lowering-*.f64 30.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right) \]

   8. Simplified 30.4%

      \[\leadsto \color{blue}{\left(a \cdot y3\right) \cdot \left(y1 \cdot z - y \cdot y5\right)} \]

   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 28.5%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 28.5%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.8e19 < z < 1.94999999999999985e157

   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 c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(c, \left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\left(\left(-1 \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y0} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y0 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot i\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]
   7. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(\color{blue}{y4} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \left(y3 \cdot z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \left(\color{blue}{y} \cdot y3\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y2\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y2\right), \mathsf{*.f64}\left(y, \color{blue}{y3}\right)\right)\right)\right)\right) \]

   8. Simplified 36.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   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. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{\left(y0 \cdot y2\right)}\right)\right) \]

       3. *-lowering-*.f64 21.2%

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y0, \color{blue}{y2}\right)\right)\right) \]

   11. Simplified 21.2%

       \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+157}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 19.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.35e-158)
   (* b (* (* x y) a))
   (if (<= b 3.8e+176) (* a (* y1 (* z y3))) (* a (* (* x y) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.35e-158) {
		tmp = b * ((x * y) * a);
	} else if (b <= 3.8e+176) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.35d-158)) then
        tmp = b * ((x * y) * a)
    else if (b <= 3.8d+176) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.35e-158) {
		tmp = b * ((x * y) * a);
	} else if (b <= 3.8e+176) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.35e-158:
		tmp = b * ((x * y) * a)
	elif b <= 3.8e+176:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.35e-158)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (b <= 3.8e+176)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.35e-158)
		tmp = b * ((x * y) * a);
	elseif (b <= 3.8e+176)
		tmp = a * (y1 * (z * y3));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.35e-158], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+176], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3499999999999999e-158

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 29.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 29.1%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       2. *-lowering-*.f64 20.3%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 20.3%

       \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]

   if -1.3499999999999999e-158 < b < 3.8000000000000003e176

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y3\right) \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a 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. associate-*r* N/A

         \[\leadsto \left(a \cdot y3\right) \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{y1 \cdot z} - y \cdot y5\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right) \]

      6. *-lowering-*.f64 25.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right) \]

   8. Simplified 25.9%

      \[\leadsto \color{blue}{\left(a \cdot y3\right) \cdot \left(y1 \cdot z - y \cdot y5\right)} \]

   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 21.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 21.3%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if 3.8000000000000003e176 < b

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 63.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 31.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 31.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       3. *-lowering-*.f64 24.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 24.3%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 21.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b))))
   (if (<= b -9e+17) t_1 (if (<= b 4.9e+176) (* 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 = a * ((x * y) * b);
	double tmp;
	if (b <= -9e+17) {
		tmp = t_1;
	} else if (b <= 4.9e+176) {
		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 = a * ((x * y) * b)
    if (b <= (-9d+17)) then
        tmp = t_1
    else if (b <= 4.9d+176) 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 = a * ((x * y) * b);
	double tmp;
	if (b <= -9e+17) {
		tmp = t_1;
	} else if (b <= 4.9e+176) {
		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 = a * ((x * y) * b)
	tmp = 0
	if b <= -9e+17:
		tmp = t_1
	elif b <= 4.9e+176:
		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(a * Float64(Float64(x * y) * b))
	tmp = 0.0
	if (b <= -9e+17)
		tmp = t_1;
	elseif (b <= 4.9e+176)
		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 = a * ((x * y) * b);
	tmp = 0.0;
	if (b <= -9e+17)
		tmp = t_1;
	elseif (b <= 4.9e+176)
		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[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+17], t$95$1, If[LessEqual[b, 4.9e+176], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9e17 or 4.9e176 < b

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 56.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   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 37.0%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 37.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

       3. *-lowering-*.f64 25.2%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 25.2%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -9e17 < b < 4.9e176

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y3\right) \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y3\right), \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(\color{blue}{\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \color{blue}{\left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(y1 \cdot y4 - y0 \cdot y5\right)\right), \left(\color{blue}{z \cdot \left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(y1 \cdot y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \color{blue}{\left(c \cdot y0 - a \cdot y1\right)} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \left(y0 \cdot y5\right)\right)\right), \left(z \cdot \left(\color{blue}{c \cdot y0} - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \left(z \cdot \left(c \cdot y0 - \color{blue}{a \cdot y1}\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\left(z \cdot \left(c \cdot y0 - a \cdot y1\right)\right), \color{blue}{\left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(c \cdot y0 - a \cdot y1\right)\right), \left(\color{blue}{y} \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(c \cdot y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \left(a \cdot y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, y4\right), \mathsf{*.f64}\left(y0, y5\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, y0\right), \mathsf{*.f64}\left(a, y1\right)\right)\right), \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)\right) \]

   5. Simplified 34.9%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in a 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. associate-*r* N/A

         \[\leadsto \left(a \cdot y3\right) \cdot \color{blue}{\left(y1 \cdot z - y \cdot y5\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot y3\right), \color{blue}{\left(y1 \cdot z - y \cdot y5\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \left(\color{blue}{y1 \cdot z} - y \cdot y5\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\left(y1 \cdot z\right), \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \left(\color{blue}{y} \cdot y5\right)\right)\right) \]

      6. *-lowering-*.f64 24.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y3\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, z\right), \mathsf{*.f64}\left(y, \color{blue}{y5}\right)\right)\right) \]

   8. Simplified 24.5%

      \[\leadsto \color{blue}{\left(a \cdot y3\right) \cdot \left(y1 \cdot z - y \cdot y5\right)} \]

   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 18.7%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y1, \mathsf{*.f64}\left(y3, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 18.7%

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 20.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.4%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in 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 35.5%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in a around inf

   \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right)\right)\right) \]

   4. *-lowering-*.f64 23.8%

      \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

8. Simplified 23.8%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

9. Taylor expanded in x around inf

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
10. Step-by-step derivation

    1. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)}\right) \]

    2. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

    3. *-lowering-*.f64 12.1%

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

11. Simplified 12.1%

    \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

12. Final simplification 12.1%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
13. Add Preprocessing

Developer Target 1: 27.6% 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 2024161 
(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)))))