Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.8% → 40.1%

Time: 30.0s

Alternatives: 23

Speedup: 3.6×

• 89.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 40.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := y0 \cdot y5 - y1 \cdot y4\\ t_4 := j \cdot \left(y3 \cdot t\_3 + \left(t \cdot t\_1 - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_1\right) + y2 \cdot t\_2\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-253}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-159}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot t\_5 + t \cdot t\_2\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+114}:\\ \;\;\;\;y3 \cdot \left(j \cdot t\_3 + \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - z \cdot t\_5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* y0 y5) (* y1 y4)))
        (t_4 (* j (+ (* y3 t_3) (- (* t t_1) (* x (- (* b y0) (* i y1)))))))
        (t_5 (- (* c y0) (* a y1))))
   (if (<= j -1.3e+106)
     t_4
     (if (<= j -2.7e-76)
       (* b (* a (- (* x y) (* z t))))
       (if (<= j -2.1e-241)
         (* t (+ (+ (* z (- (* c i) (* a b))) (* j t_1)) (* y2 t_2)))
         (if (<= j 3.2e-253)
           (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
           (if (<= j 8e-159)
             (* y2 (+ (* k (- (* y1 y4) (* y0 y5))) (+ (* x t_5) (* t t_2))))
             (if (<= j 1.5e+114)
               (* y3 (+ (* j t_3) (- (* y (- (* c y4) (* a y5))) (* z t_5))))
               t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (y0 * y5) - (y1 * y4);
	double t_4 = j * ((y3 * t_3) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (j <= -1.3e+106) {
		tmp = t_4;
	} else if (j <= -2.7e-76) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= -2.1e-241) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_2));
	} else if (j <= 3.2e-253) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 8e-159) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_5) + (t * t_2)));
	} else if (j <= 1.5e+114) {
		tmp = y3 * ((j * t_3) + ((y * ((c * y4) - (a * y5))) - (z * t_5)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (a * y5) - (c * y4)
    t_3 = (y0 * y5) - (y1 * y4)
    t_4 = j * ((y3 * t_3) + ((t * t_1) - (x * ((b * y0) - (i * y1)))))
    t_5 = (c * y0) - (a * y1)
    if (j <= (-1.3d+106)) then
        tmp = t_4
    else if (j <= (-2.7d-76)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= (-2.1d-241)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_2))
    else if (j <= 3.2d-253) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (j <= 8d-159) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_5) + (t * t_2)))
    else if (j <= 1.5d+114) then
        tmp = y3 * ((j * t_3) + ((y * ((c * y4) - (a * y5))) - (z * t_5)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (y0 * y5) - (y1 * y4);
	double t_4 = j * ((y3 * t_3) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (j <= -1.3e+106) {
		tmp = t_4;
	} else if (j <= -2.7e-76) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= -2.1e-241) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_2));
	} else if (j <= 3.2e-253) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 8e-159) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_5) + (t * t_2)));
	} else if (j <= 1.5e+114) {
		tmp = y3 * ((j * t_3) + ((y * ((c * y4) - (a * y5))) - (z * t_5)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = (a * y5) - (c * y4)
	t_3 = (y0 * y5) - (y1 * y4)
	t_4 = j * ((y3 * t_3) + ((t * t_1) - (x * ((b * y0) - (i * y1)))))
	t_5 = (c * y0) - (a * y1)
	tmp = 0
	if j <= -1.3e+106:
		tmp = t_4
	elif j <= -2.7e-76:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= -2.1e-241:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_2))
	elif j <= 3.2e-253:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif j <= 8e-159:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_5) + (t * t_2)))
	elif j <= 1.5e+114:
		tmp = y3 * ((j * t_3) + ((y * ((c * y4) - (a * y5))) - (z * t_5)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_4 = Float64(j * Float64(Float64(y3 * t_3) + Float64(Float64(t * t_1) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1))))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (j <= -1.3e+106)
		tmp = t_4;
	elseif (j <= -2.7e-76)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= -2.1e-241)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_1)) + Float64(y2 * t_2)));
	elseif (j <= 3.2e-253)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (j <= 8e-159)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * t_5) + Float64(t * t_2))));
	elseif (j <= 1.5e+114)
		tmp = Float64(y3 * Float64(Float64(j * t_3) + Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) - Float64(z * t_5))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (a * y5) - (c * y4);
	t_3 = (y0 * y5) - (y1 * y4);
	t_4 = j * ((y3 * t_3) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	t_5 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (j <= -1.3e+106)
		tmp = t_4;
	elseif (j <= -2.7e-76)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= -2.1e-241)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_2));
	elseif (j <= 3.2e-253)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (j <= 8e-159)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * t_5) + (t * t_2)));
	elseif (j <= 1.5e+114)
		tmp = y3 * ((j * t_3) + ((y * ((c * y4) - (a * y5))) - (z * t_5)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(y3 * t$95$3), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.3e+106], t$95$4, If[LessEqual[j, -2.7e-76], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-241], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-253], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-159], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$5), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+114], N[(y3 * N[(N[(j * t$95$3), $MachinePrecision] + N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.3000000000000001e106 or 1.5e114 < j

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 67.0%

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

   if -1.3000000000000001e106 < j < -2.7e-76

   1. Initial program 25.7%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

   5. Simplified 43.2%

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

   6. Taylor expanded in a around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 57.8%

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

   8. Simplified 57.8%

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

   if -2.7e-76 < j < -2.0999999999999999e-241

   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 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 66.9%

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

   if -2.0999999999999999e-241 < j < 3.1999999999999997e-253

   1. Initial program 24.0%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y4 around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      16. *-lowering-*.f64 60.9%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right)\right)\right)\right) \]

   8. Simplified 60.9%

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

   if 3.1999999999999997e-253 < j < 7.99999999999999991e-159

   1. Initial program 53.3%

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

   3. Taylor expanded in y2 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 76.5%

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

   if 7.99999999999999991e-159 < j < 1.5e114

   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 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 45.2%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-253}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-159}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+114}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y0) (* i y1)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* t_1 (- (* z k) (* x j))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* t_2 (- (* t j) (* y k))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* y1 y4) (* y0 y5)) (- (* k y2) (* j y3))))))
   (if (<= t_3 INFINITY)
     t_3
     (* j (+ (* y3 (- (* y0 y5) (* y1 y4))) (- (* t t_2) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_2) - (x * t_1)));
	}
	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 = (b * y0) - (i * y1);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_2) - (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y0) - (i * y1)
	t_2 = (b * y4) - (i * y5)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_2) - (x * 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(b * y0) - Float64(i * y1))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(t_1 * Float64(Float64(z * k) - Float64(x * j)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_2 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * Float64(Float64(k * y2) - Float64(j * y3))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(t * t_2) - Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y0) - (i * y1);
	t_2 = (b * y4) - (i * y5);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_1 * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_2) - (x * 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[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$2), $MachinePrecision] - N[(x * t$95$1), $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 93.2%

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

   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 41.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.5%

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

Alternative 3: 39.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot t\_1 - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ t_3 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_1\right) + y2 \cdot t\_3\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-250}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-150}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot t\_3\right)\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2
         (*
          j
          (+
           (* y3 (- (* y0 y5) (* y1 y4)))
           (- (* t t_1) (* x (- (* b y0) (* i y1)))))))
        (t_3 (- (* a y5) (* c y4))))
   (if (<= j -4.2e+104)
     t_2
     (if (<= j -3.5e-76)
       (* b (* a (- (* x y) (* z t))))
       (if (<= j -8.5e-242)
         (* t (+ (+ (* z (- (* c i) (* a b))) (* j t_1)) (* y2 t_3)))
         (if (<= j 4.3e-250)
           (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
           (if (<= j 1.75e-150)
             (*
              y2
              (+
               (* k (- (* y1 y4) (* y0 y5)))
               (+ (* x (- (* c y0) (* a y1))) (* t t_3))))
             (if (<= j 6.6e+93)
               (*
                y4
                (+
                 (* b (- (* t j) (* y k)))
                 (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t y2))))))
               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 = (b * y4) - (i * y5);
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	double t_3 = (a * y5) - (c * y4);
	double tmp;
	if (j <= -4.2e+104) {
		tmp = t_2;
	} else if (j <= -3.5e-76) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= -8.5e-242) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	} else if (j <= 4.3e-250) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 1.75e-150) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * t_3)));
	} else if (j <= 6.6e+93) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) - (x * ((b * y0) - (i * y1)))))
    t_3 = (a * y5) - (c * y4)
    if (j <= (-4.2d+104)) then
        tmp = t_2
    else if (j <= (-3.5d-76)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= (-8.5d-242)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3))
    else if (j <= 4.3d-250) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (j <= 1.75d-150) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * t_3)))
    else if (j <= 6.6d+93) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
    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 = (b * y4) - (i * y5);
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	double t_3 = (a * y5) - (c * y4);
	double tmp;
	if (j <= -4.2e+104) {
		tmp = t_2;
	} else if (j <= -3.5e-76) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= -8.5e-242) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	} else if (j <= 4.3e-250) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 1.75e-150) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * t_3)));
	} else if (j <= 6.6e+93) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} 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 = (b * y4) - (i * y5)
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) - (x * ((b * y0) - (i * y1)))))
	t_3 = (a * y5) - (c * y4)
	tmp = 0
	if j <= -4.2e+104:
		tmp = t_2
	elif j <= -3.5e-76:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= -8.5e-242:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3))
	elif j <= 4.3e-250:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif j <= 1.75e-150:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * t_3)))
	elif j <= 6.6e+93:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
	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(b * y4) - Float64(i * y5))
	t_2 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(t * t_1) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1))))))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (j <= -4.2e+104)
		tmp = t_2;
	elseif (j <= -3.5e-76)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= -8.5e-242)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_1)) + Float64(y2 * t_3)));
	elseif (j <= 4.3e-250)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (j <= 1.75e-150)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * t_3))));
	elseif (j <= 6.6e+93)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))));
	else
		tmp = 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 = (b * y4) - (i * y5);
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) - (x * ((b * y0) - (i * y1)))));
	t_3 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (j <= -4.2e+104)
		tmp = t_2;
	elseif (j <= -3.5e-76)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= -8.5e-242)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	elseif (j <= 4.3e-250)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (j <= 1.75e-150)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * t_3)));
	elseif (j <= 6.6e+93)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.2e+104], t$95$2, If[LessEqual[j, -3.5e-76], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-242], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.3e-250], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-150], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.6e+93], 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], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.1999999999999997e104 or 6.60000000000000017e93 < j

   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 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 65.3%

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

   if -4.1999999999999997e104 < j < -3.49999999999999997e-76

   1. Initial program 25.7%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

   5. Simplified 43.2%

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

   6. Taylor expanded in a around inf

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

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

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

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

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

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

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

      4. *-lowering-*.f64 57.8%

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

   8. Simplified 57.8%

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

   if -3.49999999999999997e-76 < j < -8.4999999999999997e-242

   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 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 66.9%

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

   if -8.4999999999999997e-242 < j < 4.30000000000000005e-250

   1. Initial program 24.0%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y4 around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      16. *-lowering-*.f64 60.9%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right)\right)\right)\right) \]

   8. Simplified 60.9%

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

   if 4.30000000000000005e-250 < j < 1.7499999999999999e-150

   1. Initial program 53.3%

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

   3. Taylor expanded in y2 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 76.5%

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

   if 1.7499999999999999e-150 < j < 6.60000000000000017e93

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-76}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-250}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-150}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+90}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)))
           (- (* t (- (* b y4) (* i y5))) (* x (- (* b y0) (* i y1))))))))
   (if (<= j -7.2e+106)
     t_1
     (if (<= j -3e-242)
       (* b (* a (- (* x y) (* z t))))
       (if (<= j 7.5e-254)
         (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
         (if (<= j 5.9e-154)
           (*
            y2
            (+
             (* k (- (* y1 y4) (* y0 y5)))
             (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4))))))
           (if (<= j 1.02e+90)
             (*
              y4
              (+
               (* b (- (* t j) (* y k)))
               (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t 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 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * ((b * y0) - (i * y1)))));
	double tmp;
	if (j <= -7.2e+106) {
		tmp = t_1;
	} else if (j <= -3e-242) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 7.5e-254) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 5.9e-154) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (j <= 1.02e+90) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * ((b * y0) - (i * y1)))))
    if (j <= (-7.2d+106)) then
        tmp = t_1
    else if (j <= (-3d-242)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= 7.5d-254) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (j <= 5.9d-154) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
    else if (j <= 1.02d+90) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * ((b * y0) - (i * y1)))));
	double tmp;
	if (j <= -7.2e+106) {
		tmp = t_1;
	} else if (j <= -3e-242) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 7.5e-254) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (j <= 5.9e-154) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (j <= 1.02e+90) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * ((b * y0) - (i * y1)))))
	tmp = 0
	if j <= -7.2e+106:
		tmp = t_1
	elif j <= -3e-242:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= 7.5e-254:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif j <= 5.9e-154:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
	elif j <= 1.02e+90:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1))))))
	tmp = 0.0
	if (j <= -7.2e+106)
		tmp = t_1;
	elseif (j <= -3e-242)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 7.5e-254)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (j <= 5.9e-154)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (j <= 1.02e+90)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))));
	else
		tmp = 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))) + ((t * ((b * y4) - (i * y5))) - (x * ((b * y0) - (i * y1)))));
	tmp = 0.0;
	if (j <= -7.2e+106)
		tmp = t_1;
	elseif (j <= -3e-242)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= 7.5e-254)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (j <= 5.9e-154)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	elseif (j <= 1.02e+90)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+106], t$95$1, If[LessEqual[j, -3e-242], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-254], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.9e-154], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e+90], 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], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.2000000000000002e106 or 1.02000000000000005e90 < j

   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 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 65.3%

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

   if -7.2000000000000002e106 < j < -3e-242

   1. Initial program 27.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

   5. Simplified 38.0%

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

   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 47.8%

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

   8. Simplified 47.8%

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

   if -3e-242 < j < 7.5000000000000005e-254

   1. Initial program 24.0%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y4 around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      16. *-lowering-*.f64 60.9%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right)\right)\right)\right) \]

   8. Simplified 60.9%

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

   if 7.5000000000000005e-254 < j < 5.9000000000000003e-154

   1. Initial program 53.3%

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

   3. Taylor expanded in y2 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 76.5%

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

   if 5.9000000000000003e-154 < j < 1.02000000000000005e90

   1. Initial program 38.2%

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

   3. Taylor expanded in y4 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+90}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_2 := b \cdot y0 - i \cdot y1\\ \mathbf{if}\;y5 \leq -450000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot t\_2\right)\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(k \cdot t\_2 - \left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{+66}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2)))))))
        (t_2 (- (* b y0) (* i y1))))
   (if (<= y5 -450000000.0)
     t_1
     (if (<= y5 2.1e-284)
       (*
        j
        (+
         (* y3 (- (* y0 y5) (* y1 y4)))
         (- (* t (- (* b y4) (* i y5))) (* x t_2))))
       (if (<= y5 3.5e-95)
         (*
          z
          (-
           (* k t_2)
           (+ (* t (- (* a b) (* c i))) (* y3 (- (* c y0) (* a y1))))))
         (if (<= y5 5.3e+66)
           (*
            y4
            (+
             (* b (- (* t j) (* y k)))
             (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t 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 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double t_2 = (b * y0) - (i * y1);
	double tmp;
	if (y5 <= -450000000.0) {
		tmp = t_1;
	} else if (y5 <= 2.1e-284) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * t_2)));
	} else if (y5 <= 3.5e-95) {
		tmp = z * ((k * t_2) - ((t * ((a * b) - (c * i))) + (y3 * ((c * y0) - (a * y1)))));
	} else if (y5 <= 5.3e+66) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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) :: t_2
    real(8) :: tmp
    t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    t_2 = (b * y0) - (i * y1)
    if (y5 <= (-450000000.0d0)) then
        tmp = t_1
    else if (y5 <= 2.1d-284) then
        tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * t_2)))
    else if (y5 <= 3.5d-95) then
        tmp = z * ((k * t_2) - ((t * ((a * b) - (c * i))) + (y3 * ((c * y0) - (a * y1)))))
    else if (y5 <= 5.3d+66) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double t_2 = (b * y0) - (i * y1);
	double tmp;
	if (y5 <= -450000000.0) {
		tmp = t_1;
	} else if (y5 <= 2.1e-284) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * t_2)));
	} else if (y5 <= 3.5e-95) {
		tmp = z * ((k * t_2) - ((t * ((a * b) - (c * i))) + (y3 * ((c * y0) - (a * y1)))));
	} else if (y5 <= 5.3e+66) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	t_2 = (b * y0) - (i * y1)
	tmp = 0
	if y5 <= -450000000.0:
		tmp = t_1
	elif y5 <= 2.1e-284:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * t_2)))
	elif y5 <= 3.5e-95:
		tmp = z * ((k * t_2) - ((t * ((a * b) - (c * i))) + (y3 * ((c * y0) - (a * y1)))))
	elif y5 <= 5.3e+66:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_2 = Float64(Float64(b * y0) - Float64(i * y1))
	tmp = 0.0
	if (y5 <= -450000000.0)
		tmp = t_1;
	elseif (y5 <= 2.1e-284)
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(x * t_2))));
	elseif (y5 <= 3.5e-95)
		tmp = Float64(z * Float64(Float64(k * t_2) - Float64(Float64(t * Float64(Float64(a * b) - Float64(c * i))) + Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (y5 <= 5.3e+66)
		tmp = Float64(y4 * Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	t_2 = (b * y0) - (i * y1);
	tmp = 0.0;
	if (y5 <= -450000000.0)
		tmp = t_1;
	elseif (y5 <= 2.1e-284)
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * ((b * y4) - (i * y5))) - (x * t_2)));
	elseif (y5 <= 3.5e-95)
		tmp = z * ((k * t_2) - ((t * ((a * b) - (c * i))) + (y3 * ((c * y0) - (a * y1)))));
	elseif (y5 <= 5.3e+66)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * 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[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -450000000.0], t$95$1, If[LessEqual[y5, 2.1e-284], N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.5e-95], N[(z * N[(N[(k * t$95$2), $MachinePrecision] - N[(N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.3e+66], 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], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -4.5e8 or 5.2999999999999997e66 < y5

   1. Initial program 28.2%

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

   3. Taylor expanded in 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 62.2%

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

   if -4.5e8 < y5 < 2.09999999999999991e-284

   1. Initial program 40.4%

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

   3. Taylor expanded in 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 51.4%

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

   if 2.09999999999999991e-284 < y5 < 3.4999999999999997e-95

   1. Initial program 19.0%

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

   3. Taylor expanded in 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%

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

   if 3.4999999999999997e-95 < y5 < 5.2999999999999997e66

   1. Initial program 31.2%

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

   3. Taylor expanded in 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 62.8%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -450000000:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{+66}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-230}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+185}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+221}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.1e+53)
   (*
    x
    (+
     (* y (- (* a b) (* c i)))
     (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0))))))
   (if (<= x -2.4e-230)
     (* y3 (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0)))))
     (if (<= x 7.5e+185)
       (*
        y4
        (+
         (* b (- (* t j) (* y k)))
         (+ (* y1 (- (* k y2) (* j y3))) (* c (- (* y y3) (* t y2))))))
       (if (<= x 1.25e+221)
         (* (* a y2) (- (* t y5) (* x y1)))
         (* b (* (* x y) a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+53) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (x <= -2.4e-230) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0))));
	} else if (x <= 7.5e+185) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else if (x <= 1.25e+221) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.1d+53)) then
        tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
    else if (x <= (-2.4d-230)) then
        tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0))))
    else if (x <= 7.5d+185) then
        tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
    else if (x <= 1.25d+221) then
        tmp = (a * y2) * ((t * y5) - (x * y1))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.1e+53) {
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	} else if (x <= -2.4e-230) {
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0))));
	} else if (x <= 7.5e+185) {
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	} else if (x <= 1.25e+221) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.1e+53:
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))))
	elif x <= -2.4e-230:
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0))))
	elif x <= 7.5e+185:
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))))
	elif x <= 1.25e+221:
		tmp = (a * y2) * ((t * y5) - (x * y1))
	else:
		tmp = b * ((x * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.1e+53)
		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 (x <= -2.4e-230)
		tmp = Float64(y3 * Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (x <= 7.5e+185)
		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 (x <= 1.25e+221)
		tmp = Float64(Float64(a * y2) * Float64(Float64(t * y5) - Float64(x * y1)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.1e+53)
		tmp = x * ((y * ((a * b) - (c * i))) + ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0)))));
	elseif (x <= -2.4e-230)
		tmp = y3 * ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0))));
	elseif (x <= 7.5e+185)
		tmp = y4 * ((b * ((t * j) - (y * k))) + ((y1 * ((k * y2) - (j * y3))) + (c * ((y * y3) - (t * y2)))));
	elseif (x <= 1.25e+221)
		tmp = (a * y2) * ((t * y5) - (x * y1));
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.1e+53], 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[x, -2.4e-230], N[(y3 * N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+185], 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[x, 1.25e+221], N[(N[(a * y2), $MachinePrecision] * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.09999999999999999e53

   1. Initial program 20.6%

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

   3. Taylor expanded in 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 59.8%

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

   if -1.09999999999999999e53 < x < -2.4000000000000002e-230

   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 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 52.3%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 54.3%

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

   8. Simplified 54.3%

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

   if -2.4000000000000002e-230 < x < 7.49999999999999955e185

   1. Initial program 34.0%

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

   3. Taylor expanded in y4 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 44.7%

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

   if 7.49999999999999955e185 < x < 1.2500000000000001e221

   1. Initial program 25.7%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

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

         \[\leadsto \mathsf{neg.f64}\left(\left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot y2\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y1\right), \mathsf{*.f64}\left(t, y5\right)\right)\right)\right) \]

   8. Simplified 76.4%

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

   if 1.2500000000000001e221 < x

   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 a around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 53.5%

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

   6. Taylor expanded in y around -inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 77.3%

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

   8. Simplified 77.3%

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

   9. Taylor expanded in b 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. *-commutative N/A

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

       4. *-lowering-*.f64 76.9%

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

   11. Simplified 76.9%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

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

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 82.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, y\right)\right), b\right) \]

   13. Applied egg-rr 82.5%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-230}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+185}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right) + \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+221}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(\frac{\left(x \cdot y\right) \cdot b}{y3} - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2900000:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-253}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+112}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -8.5e+123)
   (* a (* y3 (- (/ (* (* x y) b) y3) (* y y5))))
   (if (<= y -2900000.0)
     (*
      b
      (+
       (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
       (* y0 (- (* z k) (* x j)))))
     (if (<= y -2.8e-253)
       (*
        y2
        (+
         (* k (- (* y1 y4) (* y0 y5)))
         (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4))))))
       (if (<= y 1.3e+112)
         (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
         (* a (* y (- (* x b) (* y3 y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.5e+123) {
		tmp = a * (y3 * ((((x * y) * b) / y3) - (y * y5)));
	} else if (y <= -2900000.0) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y <= -2.8e-253) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (y <= 1.3e+112) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-8.5d+123)) then
        tmp = a * (y3 * ((((x * y) * b) / y3) - (y * y5)))
    else if (y <= (-2900000.0d0)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y <= (-2.8d-253)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
    else if (y <= 1.3d+112) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else
        tmp = a * (y * ((x * b) - (y3 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.5e+123) {
		tmp = a * (y3 * ((((x * y) * b) / y3) - (y * y5)));
	} else if (y <= -2900000.0) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y <= -2.8e-253) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	} else if (y <= 1.3e+112) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -8.5e+123:
		tmp = a * (y3 * ((((x * y) * b) / y3) - (y * y5)))
	elif y <= -2900000.0:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y <= -2.8e-253:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))))
	elif y <= 1.3e+112:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	else:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -8.5e+123)
		tmp = Float64(a * Float64(y3 * Float64(Float64(Float64(Float64(x * y) * b) / y3) - Float64(y * y5))));
	elseif (y <= -2900000.0)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y <= -2.8e-253)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (y <= 1.3e+112)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	else
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -8.5e+123)
		tmp = a * (y3 * ((((x * y) * b) / y3) - (y * y5)));
	elseif (y <= -2900000.0)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y <= -2.8e-253)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4)))));
	elseif (y <= 1.3e+112)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	else
		tmp = a * (y * ((x * b) - (y3 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -8.5e+123], N[(a * N[(y3 * N[(N[(N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision] / y3), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2900000.0], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-253], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+112], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.5e123

   1. Initial program 18.6%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 42.3%

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

   6. Taylor expanded in y around -inf

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

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

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

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

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

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

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

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

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

      5. *-lowering-*.f64 56.5%

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

   8. Simplified 56.5%

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

   9. Taylor expanded in y3 around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + \frac{b \cdot \left(x \cdot y\right)}{y3}\right)\right)}\right) \]
   10. Step-by-step derivation

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

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \left(\frac{b \cdot \left(x \cdot y\right)}{y3} + \left(\mathsf{neg}\left(y \cdot y5\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

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

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

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

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

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

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot y\right)\right), y3\right), \left(y \cdot y5\right)\right)\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(y \cdot x\right)\right), y3\right), \left(y \cdot y5\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y3, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, x\right)\right), y3\right), \left(y \cdot y5\right)\right)\right)\right) \]

       10. *-commutative N/A

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

       11. *-lowering-*.f64 60.9%

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

   11. Simplified 60.9%

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

   if -8.5e123 < y < -2.9e6

   1. Initial program 30.9%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

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

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

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

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

   5. Simplified 58.0%

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

   if -2.9e6 < y < -2.80000000000000006e-253

   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 y2 around inf

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

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

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   5. Simplified 49.1%

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

   if -2.80000000000000006e-253 < y < 1.3e112

   1. Initial program 34.8%

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

   3. Taylor expanded in y1 around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

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

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

      11. *-commutative N/A

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

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

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

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

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

   5. Simplified 44.8%

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

   6. Taylor expanded in y4 around 0

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

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

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

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

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

      16. *-lowering-*.f64 44.9%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right)\right)\right)\right) \]

   8. Simplified 44.9%

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

   if 1.3e112 < y

   1. Initial program 25.0%

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

   3. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

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

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

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

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

      4. associate--l+ N/A

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

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

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

      6. associate-*r* N/A

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

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

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

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

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

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

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

      10. *-commutative N/A

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

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

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

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

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

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

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

   5. Simplified 33.7%

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

   6. Taylor expanded in y around -inf

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 56.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(\frac{\left(x \cdot y\right) \cdot b}{y3} - y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2900000:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-253}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+112}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+198}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= t -6.5e+124)
     t_1
     (if (<= t -1.4e-92)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= t 2.4e+61)
         (* y1 (+ (* i (- (* x j) (* z k))) (* a (- (* z y3) (* x y2)))))
         (if (<= t 2.05e+198) (* (* a y2) (- (* t y5) (* x y1))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -6.5e+124) {
		tmp = t_1;
	} else if (t <= -1.4e-92) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 2.4e+61) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (t <= 2.05e+198) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (t <= (-6.5d+124)) then
        tmp = t_1
    else if (t <= (-1.4d-92)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 2.4d+61) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
    else if (t <= 2.05d+198) then
        tmp = (a * y2) * ((t * y5) - (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -6.5e+124) {
		tmp = t_1;
	} else if (t <= -1.4e-92) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 2.4e+61) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	} else if (t <= 2.05e+198) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if t <= -6.5e+124:
		tmp = t_1
	elif t <= -1.4e-92:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 2.4e+61:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))))
	elif t <= 2.05e+198:
		tmp = (a * y2) * ((t * y5) - (x * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (t <= -6.5e+124)
		tmp = t_1;
	elseif (t <= -1.4e-92)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 2.4e+61)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (t <= 2.05e+198)
		tmp = Float64(Float64(a * y2) * Float64(Float64(t * y5) - Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (t <= -6.5e+124)
		tmp = t_1;
	elseif (t <= -1.4e-92)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 2.4e+61)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (a * ((z * y3) - (x * y2))));
	elseif (t <= 2.05e+198)
		tmp = (a * y2) * ((t * y5) - (x * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+124], t$95$1, If[LessEqual[t, -1.4e-92], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+61], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+198], N[(N[(a * y2), $MachinePrecision] * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.50000000000000008e124 or 2.0500000000000001e198 < t

   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 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 42.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{i} \cdot y5\right)\right)\right)\right) \]

      4. *-lowering-*.f64 56.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 56.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -6.50000000000000008e124 < t < -1.4e-92

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(a \cdot y\right), \color{blue}{\left(j \cdot y0\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{j} \cdot y0\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{*.f64}\left(j, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.4e-92 < t < 2.3999999999999999e61

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y1\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in y4 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto y1 \cdot \color{blue}{\left(\mathsf{neg}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y1 \cdot \left(-1 \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \left(\mathsf{neg}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y2 - y3 \cdot z\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y2\right), \left(y3 \cdot z\right)\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y2 \cdot x\right), \left(y3 \cdot z\right)\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \left(y3 \cdot z\right)\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \left(j \cdot x - k \cdot z\right)\right)\right)\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(j \cdot x\right), \left(k \cdot z\right)\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \left(k \cdot z\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 45.7%

          \[\leadsto \mathsf{*.f64}\left(y1, \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y2, x\right), \mathsf{*.f64}\left(y3, z\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, z\right)\right)\right)\right)\right)\right) \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-\left(a \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   if 2.3999999999999999e61 < t < 2.0500000000000001e198

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot y2\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot y2\right), \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y1\right), \left(t \cdot y5\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y1\right), \left(t \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 64.9%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y1\right), \mathsf{*.f64}\left(t, y5\right)\right)\right)\right) \]

   8. Simplified 64.9%

      \[\leadsto \color{blue}{-\left(a \cdot y2\right) \cdot \left(x \cdot y1 - t \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+198}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+201}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= t -3.9e+124)
     t_1
     (if (<= t -2.1e-119)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= t 9e+66)
         (* i (* y1 (- (* x j) (* z k))))
         (if (<= t 9.4e+201) (* (* a y2) (- (* t y5) (* x y1))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -3.9e+124) {
		tmp = t_1;
	} else if (t <= -2.1e-119) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 9e+66) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (t <= 9.4e+201) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (t <= (-3.9d+124)) then
        tmp = t_1
    else if (t <= (-2.1d-119)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 9d+66) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (t <= 9.4d+201) then
        tmp = (a * y2) * ((t * y5) - (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -3.9e+124) {
		tmp = t_1;
	} else if (t <= -2.1e-119) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 9e+66) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (t <= 9.4e+201) {
		tmp = (a * y2) * ((t * y5) - (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if t <= -3.9e+124:
		tmp = t_1
	elif t <= -2.1e-119:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 9e+66:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif t <= 9.4e+201:
		tmp = (a * y2) * ((t * y5) - (x * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (t <= -3.9e+124)
		tmp = t_1;
	elseif (t <= -2.1e-119)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 9e+66)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (t <= 9.4e+201)
		tmp = Float64(Float64(a * y2) * Float64(Float64(t * y5) - Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (t <= -3.9e+124)
		tmp = t_1;
	elseif (t <= -2.1e-119)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 9e+66)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (t <= 9.4e+201)
		tmp = (a * y2) * ((t * y5) - (x * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+124], t$95$1, If[LessEqual[t, -2.1e-119], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+66], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.4e+201], N[(N[(a * y2), $MachinePrecision] * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.9e124 or 9.3999999999999995e201 < t

   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 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 42.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{i} \cdot y5\right)\right)\right)\right) \]

      4. *-lowering-*.f64 56.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 56.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -3.9e124 < t < -2.1e-119

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(a \cdot y\right), \color{blue}{\left(j \cdot y0\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{j} \cdot y0\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{*.f64}\left(j, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 49.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -2.1e-119 < t < 8.9999999999999997e66

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y1\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \left(\color{blue}{k} \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 40.4%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 40.4%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 8.9999999999999997e66 < t < 9.3999999999999995e201

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot y2\right) \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot y2\right), \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \left(x \cdot y1 - t \cdot y5\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\left(x \cdot y1\right), \left(t \cdot y5\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y1\right), \left(t \cdot y5\right)\right)\right)\right) \]

      8. *-lowering-*.f64 67.3%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, y2\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y1\right), \mathsf{*.f64}\left(t, y5\right)\right)\right)\right) \]

   8. Simplified 67.3%

      \[\leadsto \color{blue}{-\left(a \cdot y2\right) \cdot \left(x \cdot y1 - t \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+66}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+201}:\\ \;\;\;\;\left(a \cdot y2\right) \cdot \left(t \cdot y5 - x \cdot y1\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 21.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{+172}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-255}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(0 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.9e+172)
   (* y3 (* j (- 0.0 (* y1 y4))))
   (if (<= j -7e-80)
     (* (* y b) (* x a))
     (if (<= j -4.5e-255)
       (* c (* y4 (- 0.0 (* t y2))))
       (if (<= j 1.1e+30) (* a (* y (* x b))) (* i (* y1 (* x j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.9e+172) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -7e-80) {
		tmp = (y * b) * (x * a);
	} else if (j <= -4.5e-255) {
		tmp = c * (y4 * (0.0 - (t * y2)));
	} else if (j <= 1.1e+30) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.9d+172)) then
        tmp = y3 * (j * (0.0d0 - (y1 * y4)))
    else if (j <= (-7d-80)) then
        tmp = (y * b) * (x * a)
    else if (j <= (-4.5d-255)) then
        tmp = c * (y4 * (0.0d0 - (t * y2)))
    else if (j <= 1.1d+30) then
        tmp = a * (y * (x * b))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.9e+172) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -7e-80) {
		tmp = (y * b) * (x * a);
	} else if (j <= -4.5e-255) {
		tmp = c * (y4 * (0.0 - (t * y2)));
	} else if (j <= 1.1e+30) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.9e+172:
		tmp = y3 * (j * (0.0 - (y1 * y4)))
	elif j <= -7e-80:
		tmp = (y * b) * (x * a)
	elif j <= -4.5e-255:
		tmp = c * (y4 * (0.0 - (t * y2)))
	elif j <= 1.1e+30:
		tmp = a * (y * (x * b))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.9e+172)
		tmp = Float64(y3 * Float64(j * Float64(0.0 - Float64(y1 * y4))));
	elseif (j <= -7e-80)
		tmp = Float64(Float64(y * b) * Float64(x * a));
	elseif (j <= -4.5e-255)
		tmp = Float64(c * Float64(y4 * Float64(0.0 - Float64(t * y2))));
	elseif (j <= 1.1e+30)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.9e+172)
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	elseif (j <= -7e-80)
		tmp = (y * b) * (x * a);
	elseif (j <= -4.5e-255)
		tmp = c * (y4 * (0.0 - (t * y2)));
	elseif (j <= 1.1e+30)
		tmp = a * (y * (x * b));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.9e+172], N[(y3 * N[(j * N[(0.0 - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7e-80], N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-255], N[(c * N[(y4 * N[(0.0 - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+30], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.89999999999999985e172

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 32.6%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 43.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 43.0%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right) \cdot \color{blue}{y3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right), \color{blue}{y3}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right), y1\right), y3\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z - j \cdot y4\right), y1\right), y3\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      8. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{*.f64}\left(j, y4\right)\right), y1\right), y3\right) \]

   10. Applied egg-rr 49.1%

       \[\leadsto \color{blue}{\left(\left(a \cdot z - j \cdot y4\right) \cdot y1\right) \cdot y3} \]

   11. Taylor expanded in a around 0

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y4\right)\right)\right)}, y3\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(0 - j \cdot \left(y1 \cdot y4\right)\right), y3\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       5. *-lowering-*.f64 45.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, y4\right)\right)\right), y3\right) \]

   13. Simplified 45.9%

       \[\leadsto \color{blue}{\left(0 - j \cdot \left(y1 \cdot y4\right)\right)} \cdot y3 \]

   if -1.89999999999999985e172 < j < -7.00000000000000029e-80

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 47.6%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 28.6%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 28.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(b \cdot \left(y \cdot x\right)\right) \cdot \color{blue}{a} \]

       2. associate-*r* N/A

          \[\leadsto \left(\left(b \cdot y\right) \cdot x\right) \cdot a \]

       3. associate-*l* N/A

          \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\left(x \cdot a\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y\right), \left(\color{blue}{x} \cdot a\right)\right) \]

       6. *-lowering-*.f64 37.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right) \]

   13. Applied egg-rr 37.1%

       \[\leadsto \color{blue}{\left(b \cdot y\right) \cdot \left(x \cdot a\right)} \]

   if -7.00000000000000029e-80 < j < -4.49999999999999979e-255

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 33.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y2\right) \cdot y4\right)\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(\mathsf{neg}\left(t \cdot y2\right)\right) \cdot \color{blue}{y4}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(t \cdot y2\right)\right), \color{blue}{y4}\right)\right) \]

       9. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(0 - t \cdot y2\right), y4\right)\right) \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y2\right)\right), y4\right)\right) \]

       11. *-lowering-*.f64 33.9%

           \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, y2\right)\right), y4\right)\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{c \cdot \left(\left(0 - t \cdot y2\right) \cdot y4\right)} \]

   if -4.49999999999999979e-255 < j < 1.1e30

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 38.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 27.8%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if 1.1e30 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 62.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 45.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 43.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{+172}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-255}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(0 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 21.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.3 \cdot 10^{+169}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(0 - y1 \cdot y3\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-256}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(0 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -5.3e+169)
   (* (* j y4) (- 0.0 (* y1 y3)))
   (if (<= j -3.7e-78)
     (* (* y b) (* x a))
     (if (<= j -1.15e-256)
       (* c (* y4 (- 0.0 (* t y2))))
       (if (<= j 2.7e+30) (* a (* y (* x b))) (* i (* y1 (* x j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -5.3e+169) {
		tmp = (j * y4) * (0.0 - (y1 * y3));
	} else if (j <= -3.7e-78) {
		tmp = (y * b) * (x * a);
	} else if (j <= -1.15e-256) {
		tmp = c * (y4 * (0.0 - (t * y2)));
	} else if (j <= 2.7e+30) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-5.3d+169)) then
        tmp = (j * y4) * (0.0d0 - (y1 * y3))
    else if (j <= (-3.7d-78)) then
        tmp = (y * b) * (x * a)
    else if (j <= (-1.15d-256)) then
        tmp = c * (y4 * (0.0d0 - (t * y2)))
    else if (j <= 2.7d+30) then
        tmp = a * (y * (x * b))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -5.3e+169) {
		tmp = (j * y4) * (0.0 - (y1 * y3));
	} else if (j <= -3.7e-78) {
		tmp = (y * b) * (x * a);
	} else if (j <= -1.15e-256) {
		tmp = c * (y4 * (0.0 - (t * y2)));
	} else if (j <= 2.7e+30) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -5.3e+169:
		tmp = (j * y4) * (0.0 - (y1 * y3))
	elif j <= -3.7e-78:
		tmp = (y * b) * (x * a)
	elif j <= -1.15e-256:
		tmp = c * (y4 * (0.0 - (t * y2)))
	elif j <= 2.7e+30:
		tmp = a * (y * (x * b))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -5.3e+169)
		tmp = Float64(Float64(j * y4) * Float64(0.0 - Float64(y1 * y3)));
	elseif (j <= -3.7e-78)
		tmp = Float64(Float64(y * b) * Float64(x * a));
	elseif (j <= -1.15e-256)
		tmp = Float64(c * Float64(y4 * Float64(0.0 - Float64(t * y2))));
	elseif (j <= 2.7e+30)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -5.3e+169)
		tmp = (j * y4) * (0.0 - (y1 * y3));
	elseif (j <= -3.7e-78)
		tmp = (y * b) * (x * a);
	elseif (j <= -1.15e-256)
		tmp = c * (y4 * (0.0 - (t * y2)));
	elseif (j <= 2.7e+30)
		tmp = a * (y * (x * b));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -5.3e+169], N[(N[(j * y4), $MachinePrecision] * N[(0.0 - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-78], N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.15e-256], N[(c * N[(y4 * N[(0.0 - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+30], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.2999999999999999e169

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 32.6%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 43.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 43.0%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]

   9. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(j \cdot \left(-1 \cdot \color{blue}{y4}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{*.f64}\left(j, \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{*.f64}\left(j, \left(\mathsf{neg}\left(y4\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{*.f64}\left(j, \left(0 - \color{blue}{y4}\right)\right)\right) \]

       7. --lowering--.f64 43.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(0, \color{blue}{y4}\right)\right)\right) \]

   11. Simplified 43.0%

       \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(j \cdot \left(0 - y4\right)\right)} \]

   if -5.2999999999999999e169 < j < -3.70000000000000006e-78

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 47.6%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 28.6%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 28.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(b \cdot \left(y \cdot x\right)\right) \cdot \color{blue}{a} \]

       2. associate-*r* N/A

          \[\leadsto \left(\left(b \cdot y\right) \cdot x\right) \cdot a \]

       3. associate-*l* N/A

          \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\left(x \cdot a\right)} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\left(x \cdot a\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y\right), \left(\color{blue}{x} \cdot a\right)\right) \]

       6. *-lowering-*.f64 37.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, y\right), \mathsf{*.f64}\left(x, \color{blue}{a}\right)\right) \]

   13. Applied egg-rr 37.1%

       \[\leadsto \color{blue}{\left(b \cdot y\right) \cdot \left(x \cdot a\right)} \]

   if -3.70000000000000006e-78 < j < -1.15e-256

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \left(b \cdot \left(j \cdot t - k \cdot y\right) + \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\left(b \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(j \cdot t - k \cdot y\right)\right), \left(\color{blue}{y1 \cdot \left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \color{blue}{\left(k \cdot y2 - j \cdot y3\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right), \left(y1 \cdot \left(\color{blue}{k \cdot y2} - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \left(y1 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \color{blue}{\left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right)\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(t \cdot y2\right), \color{blue}{\left(y \cdot y3\right)}\right)\right)\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(t \cdot j - k \cdot y\right) + \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y2 around inf

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y2 \cdot y4\right) \cdot \color{blue}{\left(k \cdot y1 - c \cdot t\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y2 \cdot y4\right), \color{blue}{\left(k \cdot y1 - c \cdot t\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \left(\color{blue}{k \cdot y1} - c \cdot t\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y1\right), \color{blue}{\left(c \cdot t\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \left(\color{blue}{c} \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 33.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y2, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y1\right), \mathsf{*.f64}\left(c, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 33.5%

      \[\leadsto \color{blue}{\left(y2 \cdot y4\right) \cdot \left(k \cdot y1 - c \cdot t\right)} \]

   9. Taylor expanded in k around 0

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto c \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(t \cdot \left(y2 \cdot y4\right)\right)\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\mathsf{neg}\left(\left(t \cdot y2\right) \cdot y4\right)\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(c, \left(\left(\mathsf{neg}\left(t \cdot y2\right)\right) \cdot \color{blue}{y4}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(t \cdot y2\right)\right), \color{blue}{y4}\right)\right) \]

       9. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\left(0 - t \cdot y2\right), y4\right)\right) \]

       10. --lowering--.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(t \cdot y2\right)\right), y4\right)\right) \]

       11. *-lowering-*.f64 33.9%

           \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, y2\right)\right), y4\right)\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{c \cdot \left(\left(0 - t \cdot y2\right) \cdot y4\right)} \]

   if -1.15e-256 < j < 2.6999999999999999e30

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 38.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 27.8%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if 2.6999999999999999e30 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 62.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 45.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 43.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.3 \cdot 10^{+169}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(0 - y1 \cdot y3\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-78}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-256}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(0 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= t -3.7e+124)
     t_1
     (if (<= t -1.75e-118)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= t 3.7e+74) (* i (* y1 (- (* 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 * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -3.7e+124) {
		tmp = t_1;
	} else if (t <= -1.75e-118) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 3.7e+74) {
		tmp = i * (y1 * ((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) :: tmp
    t_1 = j * (t * ((b * y4) - (i * y5)))
    if (t <= (-3.7d+124)) then
        tmp = t_1
    else if (t <= (-1.75d-118)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 3.7d+74) then
        tmp = i * (y1 * ((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 * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (t <= -3.7e+124) {
		tmp = t_1;
	} else if (t <= -1.75e-118) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 3.7e+74) {
		tmp = i * (y1 * ((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 * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if t <= -3.7e+124:
		tmp = t_1
	elif t <= -1.75e-118:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 3.7e+74:
		tmp = i * (y1 * ((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(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (t <= -3.7e+124)
		tmp = t_1;
	elseif (t <= -1.75e-118)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 3.7e+74)
		tmp = Float64(i * Float64(y1 * 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 * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (t <= -3.7e+124)
		tmp = t_1;
	elseif (t <= -1.75e-118)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 3.7e+74)
		tmp = i * (y1 * ((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[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+124], t$95$1, If[LessEqual[t, -1.75e-118], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+74], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.70000000000000008e124 or 3.7000000000000001e74 < t

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 46.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot y4\right), \color{blue}{\left(i \cdot y5\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \left(\color{blue}{i} \cdot y5\right)\right)\right)\right) \]

      4. *-lowering-*.f64 52.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, y4\right), \mathsf{*.f64}\left(i, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 52.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -3.70000000000000008e124 < t < -1.75e-118

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(a \cdot y\right), \color{blue}{\left(j \cdot y0\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{j} \cdot y0\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{*.f64}\left(j, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 49.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.75e-118 < t < 3.7000000000000001e74

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y1\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot y1\right), \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right), \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a \cdot \left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \left(k \cdot y2 - j \cdot y3\right)\right), \left(\color{blue}{a} \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\left(k \cdot y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(j \cdot y3\right)\right)\right), \left(a \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \left(y3 \cdot j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \left(a \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y1\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, y4\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(k, y2\right), \mathsf{*.f64}\left(y3, j\right)\right)\right), \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right)\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot y4\right) \cdot \left(k \cdot y2 - y3 \cdot j\right) + \left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   6. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \left(\color{blue}{k} \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 40.6%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(y1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, x\right), \mathsf{*.f64}\left(k, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 40.6%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+182}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.68 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3.6e+182)
   (* y3 (* j (- 0.0 (* y1 y4))))
   (if (<= j -1.35e-241)
     (* b (* a (- (* x y) (* z t))))
     (if (<= j 1.68e+127)
       (* a (* y (- (* x b) (* y3 y5))))
       (* b (* j (- (* t y4) (* x y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.6e+182) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -1.35e-241) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 1.68e+127) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-3.6d+182)) then
        tmp = y3 * (j * (0.0d0 - (y1 * y4)))
    else if (j <= (-1.35d-241)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= 1.68d+127) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.6e+182) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -1.35e-241) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 1.68e+127) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -3.6e+182:
		tmp = y3 * (j * (0.0 - (y1 * y4)))
	elif j <= -1.35e-241:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= 1.68e+127:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3.6e+182)
		tmp = Float64(y3 * Float64(j * Float64(0.0 - Float64(y1 * y4))));
	elseif (j <= -1.35e-241)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 1.68e+127)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -3.6e+182)
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	elseif (j <= -1.35e-241)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= 1.68e+127)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3.6e+182], N[(y3 * N[(j * N[(0.0 - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.35e-241], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.68e+127], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.6e182

   1. Initial program 41.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   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 31.3%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 42.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right) \cdot \color{blue}{y3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right), \color{blue}{y3}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right), y1\right), y3\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z - j \cdot y4\right), y1\right), y3\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      8. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{*.f64}\left(j, y4\right)\right), y1\right), y3\right) \]

   10. Applied egg-rr 49.0%

       \[\leadsto \color{blue}{\left(\left(a \cdot z - j \cdot y4\right) \cdot y1\right) \cdot y3} \]

   11. Taylor expanded in a around 0

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y4\right)\right)\right)}, y3\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(0 - j \cdot \left(y1 \cdot y4\right)\right), y3\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       5. *-lowering-*.f64 45.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, y4\right)\right)\right), y3\right) \]

   13. Simplified 45.6%

       \[\leadsto \color{blue}{\left(0 - j \cdot \left(y1 \cdot y4\right)\right)} \cdot y3 \]

   if -3.6e182 < j < -1.35e-241

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 42.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.35e-241 < j < 1.6799999999999999e127

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 38.8%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 1.6799999999999999e127 < j

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 31.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(x \cdot y0\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\color{blue}{x} \cdot y0\right)\right)\right)\right) \]

      4. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{*.f64}\left(x, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 50.5%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+182}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.68 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+185}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -8e+185)
   (* y3 (* j (- 0.0 (* y1 y4))))
   (if (<= j -1.65e-240)
     (* b (* a (- (* x y) (* z t))))
     (if (<= j 4.9e+125)
       (* a (* y (- (* x b) (* y3 y5))))
       (* i (* y1 (* x j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -8e+185) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -1.65e-240) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 4.9e+125) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-8d+185)) then
        tmp = y3 * (j * (0.0d0 - (y1 * y4)))
    else if (j <= (-1.65d-240)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (j <= 4.9d+125) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -8e+185) {
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	} else if (j <= -1.65e-240) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (j <= 4.9e+125) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -8e+185:
		tmp = y3 * (j * (0.0 - (y1 * y4)))
	elif j <= -1.65e-240:
		tmp = b * (a * ((x * y) - (z * t)))
	elif j <= 4.9e+125:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -8e+185)
		tmp = Float64(y3 * Float64(j * Float64(0.0 - Float64(y1 * y4))));
	elseif (j <= -1.65e-240)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (j <= 4.9e+125)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -8e+185)
		tmp = y3 * (j * (0.0 - (y1 * y4)));
	elseif (j <= -1.65e-240)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (j <= 4.9e+125)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -8e+185], N[(y3 * N[(j * N[(0.0 - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-240], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.9e+125], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.9999999999999998e185

   1. Initial program 41.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   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 31.3%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 42.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right) \cdot \color{blue}{y3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right), \color{blue}{y3}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right), y1\right), y3\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z - j \cdot y4\right), y1\right), y3\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      8. *-lowering-*.f64 49.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{*.f64}\left(j, y4\right)\right), y1\right), y3\right) \]

   10. Applied egg-rr 49.0%

       \[\leadsto \color{blue}{\left(\left(a \cdot z - j \cdot y4\right) \cdot y1\right) \cdot y3} \]

   11. Taylor expanded in a around 0

       \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y4\right)\right)\right)}, y3\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(0 - j \cdot \left(y1 \cdot y4\right)\right), y3\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \left(j \cdot \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \left(y1 \cdot y4\right)\right)\right), y3\right) \]

       5. *-lowering-*.f64 45.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y1, y4\right)\right)\right), y3\right) \]

   13. Simplified 45.6%

       \[\leadsto \color{blue}{\left(0 - j \cdot \left(y1 \cdot y4\right)\right)} \cdot y3 \]

   if -7.9999999999999998e185 < j < -1.6500000000000001e-240

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in 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 42.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -1.6500000000000001e-240 < j < 4.90000000000000016e125

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.0%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 38.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 4.90000000000000016e125 < j

   1. Initial program 16.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 69.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 48.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 48.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 46.0%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+185}:\\ \;\;\;\;y3 \cdot \left(j \cdot \left(0 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 21.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y \leq -7600000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -7e+118)
   (* b (* (* x y) a))
   (if (<= y -7600000.0)
     (* b (* j (* t y4)))
     (if (<= y 1.4e+30) (* j (* i (* x y1))) (* a (* y (* 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 (y <= -7e+118) {
		tmp = b * ((x * y) * a);
	} else if (y <= -7600000.0) {
		tmp = b * (j * (t * y4));
	} else if (y <= 1.4e+30) {
		tmp = j * (i * (x * y1));
	} else {
		tmp = a * (y * (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 (y <= (-7d+118)) then
        tmp = b * ((x * y) * a)
    else if (y <= (-7600000.0d0)) then
        tmp = b * (j * (t * y4))
    else if (y <= 1.4d+30) then
        tmp = j * (i * (x * y1))
    else
        tmp = a * (y * (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 (y <= -7e+118) {
		tmp = b * ((x * y) * a);
	} else if (y <= -7600000.0) {
		tmp = b * (j * (t * y4));
	} else if (y <= 1.4e+30) {
		tmp = j * (i * (x * y1));
	} else {
		tmp = a * (y * (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 y <= -7e+118:
		tmp = b * ((x * y) * a)
	elif y <= -7600000.0:
		tmp = b * (j * (t * y4))
	elif y <= 1.4e+30:
		tmp = j * (i * (x * y1))
	else:
		tmp = a * (y * (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 (y <= -7e+118)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y <= -7600000.0)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y <= 1.4e+30)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	else
		tmp = Float64(a * Float64(y * 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 (y <= -7e+118)
		tmp = b * ((x * y) * a);
	elseif (y <= -7600000.0)
		tmp = b * (j * (t * y4));
	elseif (y <= 1.4e+30)
		tmp = j * (i * (x * y1));
	else
		tmp = a * (y * (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[y, -7e+118], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7600000.0], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+30], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000033e118

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.4%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 57.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 57.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 46.6%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 46.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto a \cdot \left(\left(y \cdot x\right) \cdot \color{blue}{b}\right) \]

       2. associate-*r* N/A

          \[\leadsto \left(a \cdot \left(y \cdot x\right)\right) \cdot \color{blue}{b} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot \left(y \cdot x\right)\right), \color{blue}{b}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(y \cdot x\right)\right), b\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y\right)\right), b\right) \]

       6. *-lowering-*.f64 48.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, y\right)\right), b\right) \]

   13. Applied egg-rr 48.7%

       \[\leadsto \color{blue}{\left(a \cdot \left(x \cdot y\right)\right) \cdot b} \]

   if -7.00000000000000033e118 < y < -7.6e6

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right), \color{blue}{\left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(\color{blue}{y0} \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(x \cdot y - t \cdot z\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \left(j \cdot t - k \cdot y\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(j \cdot t\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\left(t \cdot j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \left(k \cdot y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \left(y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \color{blue}{\left(j \cdot x - k \cdot z\right)}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(y4, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, j\right), \mathsf{*.f64}\left(k, y\right)\right)\right)\right), \mathsf{*.f64}\left(y0, \mathsf{\_.f64}\left(\left(j \cdot x\right), \color{blue}{\left(k \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 58.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(x \cdot y0\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\color{blue}{x} \cdot y0\right)\right)\right)\right) \]

      4. *-lowering-*.f64 42.5%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{*.f64}\left(x, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 42.5%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \left(y4 \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-lowering-*.f64 38.8%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y4, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 38.8%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -7.6e6 < y < 1.39999999999999992e30

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 46.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 33.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 33.0%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       2. *-lowering-*.f64 27.1%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(x, \color{blue}{y1}\right)\right)\right) \]

   11. Simplified 27.1%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]

   if 1.39999999999999992e30 < y

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 50.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 37.4%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 37.4%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y \leq -7600000:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10500000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -10500000.0)
   (* a (* (* x y) b))
   (if (<= x 2.35e-45)
     (* a (* z (* y1 y3)))
     (if (<= x 8e+136) (* b (* j (* t y4))) (* a (* y (* 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 <= -10500000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= 2.35e-45) {
		tmp = a * (z * (y1 * y3));
	} else if (x <= 8e+136) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (y * (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 <= (-10500000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (x <= 2.35d-45) then
        tmp = a * (z * (y1 * y3))
    else if (x <= 8d+136) then
        tmp = b * (j * (t * y4))
    else
        tmp = a * (y * (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 <= -10500000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= 2.35e-45) {
		tmp = a * (z * (y1 * y3));
	} else if (x <= 8e+136) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (y * (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 <= -10500000.0:
		tmp = a * ((x * y) * b)
	elif x <= 2.35e-45:
		tmp = a * (z * (y1 * y3))
	elif x <= 8e+136:
		tmp = b * (j * (t * y4))
	else:
		tmp = a * (y * (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 <= -10500000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (x <= 2.35e-45)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (x <= 8e+136)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(a * Float64(y * 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 <= -10500000.0)
		tmp = a * ((x * y) * b);
	elseif (x <= 2.35e-45)
		tmp = a * (z * (y1 * y3));
	elseif (x <= 8e+136)
		tmp = b * (j * (t * y4));
	else
		tmp = a * (y * (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, -10500000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e-45], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+136], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.05e7

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 31.4%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 44.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 44.3%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

   if -1.05e7 < x < 2.3499999999999999e-45

   1. Initial program 39.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 40.1%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 31.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right) \cdot \color{blue}{y3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right), \color{blue}{y3}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right), y1\right), y3\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z - j \cdot y4\right), y1\right), y3\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      8. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{*.f64}\left(j, y4\right)\right), y1\right), y3\right) \]

   10. Applied egg-rr 31.7%

       \[\leadsto \color{blue}{\left(\left(a \cdot z - j \cdot y4\right) \cdot y1\right) \cdot y3} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. 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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(\left(y1 \cdot y3\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 23.2%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), z\right)\right) \]

   13. Simplified 23.2%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if 2.3499999999999999e-45 < x < 8.00000000000000047e136

   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 30.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(t \cdot y4\right), \color{blue}{\left(x \cdot y0\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \left(\color{blue}{x} \cdot y0\right)\right)\right)\right) \]

      4. *-lowering-*.f64 40.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, y4\right), \mathsf{*.f64}\left(x, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 40.9%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \color{blue}{\left(t \cdot y4\right)}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \left(y4 \cdot \color{blue}{t}\right)\right)\right) \]

       4. *-lowering-*.f64 33.9%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(y4, \color{blue}{t}\right)\right)\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 8.00000000000000047e136 < x

   1. Initial program 18.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 41.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 48.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 48.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 46.1%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 46.1%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10500000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3.5e+47)
   (* j (* i (* x y1)))
   (if (<= j 3.4e+123)
     (* a (* y (- (* x b) (* y3 y5))))
     (* i (* y1 (* x j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.5e+47) {
		tmp = j * (i * (x * y1));
	} else if (j <= 3.4e+123) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-3.5d+47)) then
        tmp = j * (i * (x * y1))
    else if (j <= 3.4d+123) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.5e+47) {
		tmp = j * (i * (x * y1));
	} else if (j <= 3.4e+123) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -3.5e+47:
		tmp = j * (i * (x * y1))
	elif j <= 3.4e+123:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3.5e+47)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (j <= 3.4e+123)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -3.5e+47)
		tmp = j * (i * (x * y1));
	elseif (j <= 3.4e+123)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3.5e+47], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+123], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.50000000000000015e47

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 39.2%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 39.2%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       2. *-lowering-*.f64 32.9%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(x, \color{blue}{y1}\right)\right)\right) \]

   11. Simplified 32.9%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]

   if -3.50000000000000015e47 < j < 3.40000000000000001e123

   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 a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if 3.40000000000000001e123 < j

   1. Initial program 16.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 69.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 48.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 48.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 46.0%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3.6e+47)
   (* j (* i (* x y1)))
   (if (<= j 1.45e+30) (* y (* x (* a b))) (* i (* y1 (* x j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.6e+47) {
		tmp = j * (i * (x * y1));
	} else if (j <= 1.45e+30) {
		tmp = y * (x * (a * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-3.6d+47)) then
        tmp = j * (i * (x * y1))
    else if (j <= 1.45d+30) then
        tmp = y * (x * (a * b))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.6e+47) {
		tmp = j * (i * (x * y1));
	} else if (j <= 1.45e+30) {
		tmp = y * (x * (a * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -3.6e+47:
		tmp = j * (i * (x * y1))
	elif j <= 1.45e+30:
		tmp = y * (x * (a * b))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3.6e+47)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (j <= 1.45e+30)
		tmp = Float64(y * Float64(x * Float64(a * b)));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -3.6e+47)
		tmp = j * (i * (x * y1));
	elseif (j <= 1.45e+30)
		tmp = y * (x * (a * b));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3.6e+47], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+30], N[(y * N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.60000000000000008e47

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 39.2%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 39.2%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       2. *-lowering-*.f64 32.9%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(x, \color{blue}{y1}\right)\right)\right) \]

   11. Simplified 32.9%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]

   if -3.60000000000000008e47 < j < 1.4499999999999999e30

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 25.8%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 25.8%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

       2. *-commutative N/A

          \[\leadsto \left(a \cdot b\right) \cdot \left(x \cdot \color{blue}{y}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\left(a \cdot b\right) \cdot x\right) \cdot \color{blue}{y} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot b\right) \cdot x\right), \color{blue}{y}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot b\right), x\right), y\right) \]

       6. *-lowering-*.f64 27.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), x\right), y\right) \]

   13. Applied egg-rr 27.7%

       \[\leadsto \color{blue}{\left(\left(a \cdot b\right) \cdot x\right) \cdot y} \]

   if 1.4499999999999999e30 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 62.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 45.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 43.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 20.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -6.2e+45)
   (* j (* i (* x y1)))
   (if (<= j 5.5e+27) (* a (* y (* x b))) (* i (* y1 (* x j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+45) {
		tmp = j * (i * (x * y1));
	} else if (j <= 5.5e+27) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-6.2d+45)) then
        tmp = j * (i * (x * y1))
    else if (j <= 5.5d+27) then
        tmp = a * (y * (x * b))
    else
        tmp = i * (y1 * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -6.2e+45) {
		tmp = j * (i * (x * y1));
	} else if (j <= 5.5e+27) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -6.2e+45:
		tmp = j * (i * (x * y1))
	elif j <= 5.5e+27:
		tmp = a * (y * (x * b))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -6.2e+45)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (j <= 5.5e+27)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -6.2e+45)
		tmp = j * (i * (x * y1));
	elseif (j <= 5.5e+27)
		tmp = a * (y * (x * b));
	else
		tmp = i * (y1 * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -6.2e+45], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e+27], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.19999999999999975e45

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 54.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 39.2%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 39.2%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)}\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

       2. *-lowering-*.f64 32.9%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(x, \color{blue}{y1}\right)\right)\right) \]

   11. Simplified 32.9%

       \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(x \cdot y1\right)\right)} \]

   if -6.19999999999999975e45 < j < 5.49999999999999966e27

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.0%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 27.0%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

   if 5.49999999999999966e27 < j

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 62.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 45.6%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 43.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 43.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))))
   (if (<= j -1e+47) t_1 (if (<= j 2.5e+29) (* a (* y (* x 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 = i * (y1 * (x * j));
	double tmp;
	if (j <= -1e+47) {
		tmp = t_1;
	} else if (j <= 2.5e+29) {
		tmp = a * (y * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y1 * (x * j))
    if (j <= (-1d+47)) then
        tmp = t_1
    else if (j <= 2.5d+29) then
        tmp = a * (y * (x * 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 = i * (y1 * (x * j));
	double tmp;
	if (j <= -1e+47) {
		tmp = t_1;
	} else if (j <= 2.5e+29) {
		tmp = a * (y * (x * 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 = i * (y1 * (x * j))
	tmp = 0
	if j <= -1e+47:
		tmp = t_1
	elif j <= 2.5e+29:
		tmp = a * (y * (x * 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(i * Float64(y1 * Float64(x * j)))
	tmp = 0.0
	if (j <= -1e+47)
		tmp = t_1;
	elseif (j <= 2.5e+29)
		tmp = Float64(a * Float64(y * Float64(x * 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 = i * (y1 * (x * j));
	tmp = 0.0;
	if (j <= -1e+47)
		tmp = t_1;
	elseif (j <= 2.5e+29)
		tmp = a * (y * (x * 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[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+47], t$95$1, If[LessEqual[j, 2.5e+29], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -1e47 or 2.5e29 < j

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   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 59.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right)} \]

   6. Taylor expanded in 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 42.9%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, y1\right), \mathsf{*.f64}\left(b, \color{blue}{y0}\right)\right)\right)\right) \]

   8. Simplified 42.9%

      \[\leadsto j \cdot \color{blue}{\left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(\left(j \cdot x\right) \cdot \color{blue}{y1}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\left(j \cdot x\right), \color{blue}{y1}\right)\right) \]

       4. *-lowering-*.f64 39.0%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, x\right), y1\right)\right) \]

   11. Simplified 39.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -1e47 < j < 2.5e29

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 39.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 27.0%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 27.0%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+47}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4000000000.0)
   (* a (* (* x y) b))
   (if (<= x 9e-32) (* a (* z (* y1 y3))) (* a (* y (* 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 <= -4000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= 9e-32) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = a * (y * (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 <= (-4000000000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (x <= 9d-32) then
        tmp = a * (z * (y1 * y3))
    else
        tmp = a * (y * (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 <= -4000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= 9e-32) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = a * (y * (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 <= -4000000000.0:
		tmp = a * ((x * y) * b)
	elif x <= 9e-32:
		tmp = a * (z * (y1 * y3))
	else:
		tmp = a * (y * (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 <= -4000000000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (x <= 9e-32)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	else
		tmp = Float64(a * Float64(y * 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 <= -4000000000.0)
		tmp = a * ((x * y) * b);
	elseif (x <= 9e-32)
		tmp = a * (z * (y1 * y3));
	else
		tmp = a * (y * (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, -4000000000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-32], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4e9

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 31.4%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 49.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b 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. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

       4. *-lowering-*.f64 44.3%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 44.3%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

   if -4e9 < x < 9.00000000000000009e-32

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in 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 39.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y3\right) \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(z \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(y1 \cdot y3\right) \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right) + a \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(\color{blue}{-1 \cdot \left(j \cdot y4\right)} + a \cdot z\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \left(a \cdot z + \color{blue}{-1 \cdot \left(j \cdot y4\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\left(a \cdot z\right), \color{blue}{\left(-1 \cdot \left(j \cdot y4\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\color{blue}{-1} \cdot \left(j \cdot y4\right)\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right)\right) \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\left(j \cdot y4\right)\right)\right)\right) \]

      9. *-lowering-*.f64 31.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y4\right)\right)\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z + \left(-j \cdot y4\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot \color{blue}{\left(y1 \cdot y3\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right) \cdot \color{blue}{y3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right) \cdot y1\right), \color{blue}{y3}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z + \left(\mathsf{neg}\left(j \cdot y4\right)\right)\right), y1\right), y3\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(a \cdot z - j \cdot y4\right), y1\right), y3\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \left(j \cdot y4\right)\right), y1\right), y3\right) \]

      8. *-lowering-*.f64 31.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, z\right), \mathsf{*.f64}\left(j, y4\right)\right), y1\right), y3\right) \]

   10. Applied egg-rr 31.6%

       \[\leadsto \color{blue}{\left(\left(a \cdot z - j \cdot y4\right) \cdot y1\right) \cdot y3} \]

   11. Taylor expanded in a around inf

       \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. 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. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(\left(y1 \cdot y3\right) \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(y1 \cdot y3\right), \color{blue}{z}\right)\right) \]

       4. *-lowering-*.f64 22.5%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y1, y3\right), z\right)\right) \]

   13. Simplified 22.5%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if 9.00000000000000009e-32 < x

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

      5. *-lowering-*.f64 42.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 32.5%

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 32.5%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* 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) {
	return a * (y * (x * 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 * (y * (x * 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 * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   6. associate-*r* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

5. Simplified 38.3%

   \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

   5. *-lowering-*.f64 30.9%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

8. Simplified 30.9%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

9. Taylor expanded in b around inf

   \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x\right)}\right)\right) \]
10. Step-by-step derivation

    1. *-lowering-*.f64 21.6%

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{x}\right)\right)\right) \]

11. Simplified 21.6%

    \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x\right)}\right) \]

12. Final simplification 21.6%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]
13. Add Preprocessing

Alternative 23: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(-1 \cdot a\right), \color{blue}{\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   4. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right) + \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(-1 \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\right), \color{blue}{\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) \]

   6. associate-*r* N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\left(\left(-1 \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \left(x \cdot y - t \cdot z\right)\right), \left(\color{blue}{y1} \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)} - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(t \cdot z\right)\right)\right), \left(y1 \cdot \left(\color{blue}{x \cdot y2} - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \left(y1 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(-1, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(t, z\right)\right)\right), \mathsf{\_.f64}\left(\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right), \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right)\right) \]

5. Simplified 38.3%

   \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(\left(-1 \cdot b\right) \cdot \left(y \cdot x - t \cdot z\right) + \left(y1 \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y around -inf

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right)\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(b \cdot x\right), \color{blue}{\left(y3 \cdot y5\right)}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \left(\color{blue}{y3} \cdot y5\right)\right)\right)\right) \]

   5. *-lowering-*.f64 30.9%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, x\right), \mathsf{*.f64}\left(y3, \color{blue}{y5}\right)\right)\right)\right) \]

8. Simplified 30.9%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

9. Taylor expanded in b 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. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

    4. *-lowering-*.f64 21.3%

       \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

11. Simplified 21.3%

    \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x\right)\right)} \]

12. Final simplification 21.3%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
13. Add Preprocessing

Developer Target 1: 28.3% 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 2024158 
(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)))))